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.
1) The original function is: P(t) = 145e-0.092t
2) When solving for 70 beats per minute, you replace P(t) with the number 70:
70 = 145e-0.092t
3) Then, you divide each side of the equation by 145 to work towards isolating (t).
70/145 = 145e-0.092t/145
0.482758621 = e-0.092t
4) Then, you use the definition of a logarithm to continue to solve for t.
-0.092t = ln (0.482758621)
-0.092t = -0.7282385
5) Next, you divide each side of the equation by -0.092 to solve for t.
-0.092t/-0.092 = -0.7282385/-0.092
t = 7.91563587
6) Rounding the value of (t) to the nearest tenth of a minute:
t = 7.9 minutes or 8 minutes
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