SOLUTION: I have no idea where to start or what I am doing at all. The function P(t) = 145e-0.092t models a runner’s pulse, P(t), in beats per minute, t minutes after a race, where 0 &#

Algebra ->  Graphs -> SOLUTION: I have no idea where to start or what I am doing at all. The function P(t) = 145e-0.092t models a runner’s pulse, P(t), in beats per minute, t minutes after a race, where 0 &#      Log On


   



Question 1042241: I have no idea where to start or what I am doing at all.
The function P(t) = 145e-0.092t models a runner’s pulse, P(t), in beats per minute, t minutes after a race, where 0 ≤ t ≤15. Graph the function using a graphing utility. TRACE along the graph and determine after how many minutes the runner’s pulse will be 70 beats per minute. Round to the nearest tenth of a minute. Verify your observation algebraically.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+P%28t%29+=+145%2Ae%5E%28+-.092t+%29+
Here's the plot:
+graph%28+500%2C+500%2C+-10%2C+75%2C+-20%2C+200%2C+145%2Ae%5E%28-.092x+%29+%29+
From the plot, I would guess that +P+=+70+, after about
+8+ minutes after the race.
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Solving for +P+=+70+,
+70+=+145%2Ae%5E%28+-.092t+%29+
+.48276+=+e%5E%28+-.092t+%29+
Take the natural log of both sides
+-.728236+=+-.092t+
+t+=+7.9156+
+t+=+7.9+ ( rounded off )
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check:
+70+=+145%2Ae%5E%28+-.092t+%29+
+70+=+145%2Ae%5E%28+-.092%2A7.9156+%29+
+70+=+145%2Ae%5E%28-.72824+%29+
+70+=+145%2A.48276+
+70+=+70.0002+
close enough