Answer:
the runner’s pulse will be 70 beats per minute in 7.9 minutes
Step-by-step explanation:
[tex]P(t) = 145e^{-0.092t}[/tex]
Graph the function using a graphing utility.
Graph is attached below.
P(t) is beats per minute
Given P(t) is 70, so we plug in 70 for P(t) and solve for t
[tex]70= 145e^{-0.092t}[/tex]
Divide both sides by 145
[tex]\frac{70}{145} =e^{-0.092t}[/tex]
Now take ln on both sides
[tex]ln(\frac{70}{145})=ln(e^{-0.092t})[/tex]
[tex]ln(\frac{70}{145})=-0.092t[/tex]
Divide both sides by -0.092
So t≈7.91564
Round to nearest tenth t= 7.9
We can verify it from second graph
