Question

A quantity with an initial value of 840 decays continuously at a rate of 5% per day. What is the value of the quantity after 10 weeks, to the nearest hundredth?

Answer 1

25.37

Explanation:

Write a function:

f(t)=840e^{rt}

f(t)=840e

rt

Continuously uses Pe^(rt)

-0.05

r: decays 5%→−0.05

per day

f(t)=840e^{-0.05t}

f(t)=840e

−0.05t

(where t is in days)

10 weeks→10⋅7→70 days

There are 7 days in a week

Plug in t=70

f(70)=840e^{-0.05(70)}

f(70)=840e

−0.05(70)

25.3658020747

≈25.37