Question

A quantity with an initial value of 720 decays continuously at a rate of 9% per hour. What is the value of the quantity after 69 hours, to the nearest hundredth?

Answer 1

1.45

Explanation:

f(t)=720e^rt

f(t)=720e

rt

Continuously uses Pe^(rt)

r\text{: decays }9\% \

r: decays 9%→−0.09

per hour

f(t)=720e^{-0.09t}

f(t)=720e

−0.09t

(where t is in hours)

69\text{ hours: no time conversion necessary}

69 hours: no time conversion necessary

hours are the only units in the problem.

\text{Plug in }t=69

Plug in t=69

f(69)=720e^{-0.09(69)}

f(69)=720e

−0.09(69)

1.44665097413

1.44665097413

\approx 1.45

≈1.45

Round to the nearest hundredth