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Problem 8 Easy Difficulty

Use the model given to answer the questions about the object or process being modeled.
A mountain climber models the temperature $T$ (in $^{\circ} \mathrm{F}$ ) at elevation $h$ (in $\mathrm{ft}$ ) by
$$
T=70-0.003 h
$$
a. Find the temperature $T$ at an elevation of $1500 \mathrm{ft}$.
b. If the temperature is $64^{\circ} \mathrm{F}$, what is the elevation?

Answer

$2000 FT$

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Video Transcript

{'transcript': "So I've written out our model at the top of the screen here and part a. Ask this. You found the temperature tea at an elevation of 1,500 feet. So when we read out, our variables like this are known. H is 1,500 feet. We want to find teeth. It's really easy to see what we need to plug into the equation and solved. So we're simply going to put tea in Cools 70 Linus, 0.3 times are H fortunes 1,500 and all we have to do right now is just solve for teeth so you can do this math on your own. I've already done it. We get t equals 65.5 degrees Fahrenheit. A party is very similar. We are given the temperature is 64 degrees Fahrenheit. And now this time we're solving for our height. So the same was in part a. We're going to plug in this time 64 for our tea. So we get 64 Cool 70 linus 0.3 and then we're going to leave our H as an age because that's what we're solving for. So now, to solve for our variable. Here. We're going to some track 70 from both sides. Stephanie, my 70 and we'll get negative. Six equals negative. 0.3 h. So to isolate the H, we're going to divide both sides by are negative 0.3 left side. Negative. You're 003 and we find our solution at H equals 2,000 feet in there."}