My colleague Amy Harder takes stock of some coal industry news...

Two separate developments on Tuesday offer us a stark reminder of coal's long-term downward trajectory in the U.S., regardless of what President Trump says or does.

1. Washington state rejected a key permit for a coal export terminal in the state. That's the sixth rejection of a total of six proposed such projects in the Pacific Northwest over the last few years.

• Get smart: These rejections occurred mostly due to local and state government opposition in a liberal part of the country. Trump has no control over this.

2. Arch Coal withdrew an application for a federal coal lease in Wyoming that would have expanded the second-largest coal mine in the country, SNL reported Tuesday. Recall, the Interior Department repealed an Obama-era moratorium on federal coal leasing in March. When that temporary moratorium was first put in place in January 2016, coal companies said it didn't make a big difference, citing low demand and sufficient supply on current leases.

• Get smart: Imposing it made little difference, and lifting it is also making little difference.

Why this matters: Companies and local governments make decisions that are best for them, not the federal government. These anecdotes are some of the starkest since Trump assumed office and show the coal industry's downward trend.

Yes, but:

The Energy Information Administration

recently reported

that coal's share of electricity is expected to surpass natural gas for the next two years, which is an argument the coal industry points to as evidence the fuel is on the rise again. What the industry doesn't say is that by 2018, the two fuels are basically in a dead heat.

Exxon: Via Bloomberg, "Treasury Secretary Steven Mnuchin filed court papers in Texas denying claims by Exxon Mobil Corp. that a $2 million fine assessed against the energy company in July, over alleged "egregious" violations of sanctions against Russia three years ago, was unconstitutional."

Shell: CEO Ben van Beurden chatted with CNBC in Singapore about his outlook. "It's not unreasonable to expect that if you want to make financial projections going out in the future, you want to make projections around $60 oil by the end of the decade," he said, predicting further market tightening while emphasizing the inherent uncertainty of price forecasting.

• Overall, he said the company has transformed to be "much more resilient" in a lower price environment, noting it has more free cash flow at $60 dollars than it used to when oil was in the $90 range. He also emphasizes the company's increasing movement into natural gas.

Total: The French multinational giant has been busy lately. Yesterday brought the news that they're exploring purchase of a stake in a bloc off the coast of Guyana, not far from where Exxon is developing what appears to be a massive oil find.

• More broadly, Wood Mackenzie's latest podcast takes stock of some of their other recent moves, including their new exploration agreement with Chevron in the deepwater Gulf of Mexico and deeper entry into renewables with their purchase of a 23% stake in Eren Renewable Energy.

The satellite imagery above has been making the rounds and illustrates the crisis facing Puerto Rico after Hurricane Maria.

What's happening: "A week after Hurricane Maria ravaged Puerto Rico, the US commonwealth's residents are struggling to survive without basic necessities as federal officials say aid is still on the way," CNN reports. Lack of fuel is problem "across the island."

• "People are relying on generators to keep appliances such as air conditioners, medical devices and refrigerators running. Many hospitals are struggling to treat patients and scores of people are lining up with gas cans for hours," their story notes.
• They report that two people died in the intensive care unit of a hospital in San Juan when it ran out of diesel fuel.

Power situation: The latest Energy Department update yesterday notes "significant damage" to transmission and distribution systems.

• "The Puerto Rico Electric Power Authority (PREPA) continues to report near 100% of total customers in Puerto Rico remain without power, with the exception of facilities on generators and some critical facilities," it states.
• This ABC News piece takes stock of power restoration, noting "As of Monday night, at least 5 percent of electricity had been restored across the island."

Trump under fire: Via Politico, "Trump and his aides have found themselves on the defensive for the president's muted response to the latest storm, which devastated the island and left millions of American citizens without electricity, housing or running water."

Dyson enters the fray: The BBC reports that Sir James Dyson, the billionaire inventor of the bagless vacuum cleaner, announced Tuesday that his company is investing £2 billion ($2.7 billion) to develop and build a "radical and different" electric car. Dyson said £1 billion will be spent on developing the car, which is set to hit the streets in 2020, with the other £1 billion on making the battery.

Dyson said his company has been working on the project for two years with 400 employees, according to press accounts.

• Why it matters: The decision to go public with the firm's $2.7 billion decision to enter the electric vehicle tech field is another sign that entrepreneurs see a major growth market, especially as a number of countries are rolling out new policies to begin moving away from cars powered by fossil fuels.
• Be smart: "Dyson knows a lot about motors, batteries and consumer tastes, and has enviable R&D capability. Certainly not the craziest hat in the ring," said Bloomberg New Energy Finance EV analyst Colin McKerracher on Twitter.

Tesla's growth: Morgan Stanley analyst Adam Jonas, a longtime optimist about Tesla's potential, is out with a new forecast predicting that the number of Tesla cars on the road worldwide will be 300,000 by year's end, and will grow to 531,000 by the end of 2018.

Then? Up, up, up, reaching nearly 32 million units on the road in 2040 (including cars used in ride-sharing services). "It has been generations since the investment community witnessed such a high growth rate in the population of a single auto firm," Jonas writes.

• Yes, but: Morgan Stanley notes that Tesla's fortunes are subject to forces including the price of oil and other commodities and continued capital market willingness to fund its ambitions.

Big picture: Reuters notes that Wall Street is weighing the bullish Morgan Stanley forecast against Dyson's announcement that it's entering the EV market, heralding a new competitor for Elon Musk.

• "Shares of Tesla Inc...remained in a correction on Tuesday after a billionaire British inventor announced plans for his own electric vehicles, taking the shine off an analyst prediction that Tesla's cars would be commonplace within two years," they report.

With so much left undone: Yesterday afternoon, after GOP Sen. Lindsey Graham's 11th-hour effort to repeal parts of the Affordable Care Act collapsed, he also found time to discuss an even steeper uphill climb: legislation to price carbon.

Not long after Republicans announced they wouldn't vote on the Graham-Cassidy health care bill, Graham appeared at a National Clean Energy Week event to lay out the rationale for creating a carbon fee. A couple takeaways...

• In his brief speech and a quick gaggle with reporters, Graham repeatedly cited the need for a cash source to supplement the long-term decline in Highway Trust Fund revenues due to greater efficiency and, eventually, more widespread electrification of cars.
• "The Highway Trust Fund is falling apart. Somebody needs to do something about it," he told reporters when asked why he thinks a deal is possible.
• Graham emphasized that a carbon fee would be a pro-nuclear stance, and hinted at some of his behind-the-scenes activities as he explores potential legislation. "I am talking to some power companies. We have got to make it good business for them. Nuclear power is far more valuable in a lower-carbon economy."
• Graham sought to emphasize that he's still an advocate of domestic oil-and-gas development. "To the fossil fuel industry, we are going to do it in a business-friendly manner. Oil and gas are with us for a while to come."

Big picture: "I do believe that there is a deal to be had that will increase the GDP of America, not decrease it; that can make the planet a much more healthy place to live; and create jobs in our backyard rather than them going to China, and above all else, wean us off fossil fuels from areas of the world that are very dangerous," Graham said.

What's next: As your Generate host noted here, there are basically zero near-term and probably even medium-term prospects for the idea. A key thing to watch going forward is whether Graham can muster any GOP support for carbon pricing beyond the tiny circle of sitting GOP lawmakers who have already backed the idea in some form. So far, nobody has emerged.

Check it out: The latest edition of the Smarter Faster series from Axios features billionaire climate activist Tom Steyer on the future of batteries and how storage can enable wider renewable power deployment.

You can watch it here.