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