Mathematics: Find the relative rate of change at the given value of . Assume is in years and give your answer as a percent

Find the relative rate of change at the given value

asiababbie33

05.02.2022

84.37 %.

Step-by-step explanation:

The question is shown in the attached figure.

We have,

$f(t)=2t^3+10,\ t=3$

We can find the value of f(t) at t = 3,

$f(3)=2(3)^3+10\\\\f(3)=64$

Finding f'(t).

f'(t)=6t^2

Finding f'(t) at t = 3

$f'(3)=6(3)^2\\\\=54$

The relative change is calculated as :

$\dfrac{f'(t)}{f(t)}=\dfrac{54}{64}\\\\=0.8437$

In percentage rate of change,

$\dfrac{f'(t)}{f(t)}=0.8437\times 100\\\\=84.37\%$

Hence, the required percent change is 84.37 %.

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