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Lady_Fox [76]
3 years ago
13

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?
Mathematics
1 answer:
Pachacha [2.7K]3 years ago
7 0

Answer:

25.37

Step-by-step 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

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