Question

A quantity with an initial value of 390 decays exponentially at a rate of 8.5% every 9 weeks. What is the value of the quantity after 42 days, to the nearest hundredth?

Answer 1

The answer is 367.57

Answer 2

Explanation:

The initial value = 390

It decayed at an exponential rate of 8.5% for 9weeks which is also 63days

Decay exponential rate after 42days will be:

8.5% = 63days

x% = 42days

8.5% ×42days = 63days×x%

357 = 63x

x = 357/63

x = 5.666%

Hence after 42days it would have decayed by 5.666% of it initial value.

That is 5.666% of 390

5.666/100 × 390

0.056×390

= 22.0974

To the nearest hundredth 22.10

Hence the value left will be 390-22.0974

= 367.9026

To the nearest hundredth 367.90