Answer:
84.37 %.
Step-by-step explanation:
The question is shown in the attached figure.
We have,
[tex]f(t)=2t^3+10,\ t=3[/tex]
We can find the value of f(t) at t = 3,
[tex]f(3)=2(3)^3+10\\\\f(3)=64[/tex]
Finding f'(t).
[tex]f'(t)=6t^2[/tex]
Finding f'(t) at t = 3
[tex]f'(3)=6(3)^2\\\\=54[/tex]
The relative change is calculated as :
[tex]\dfrac{f'(t)}{f(t)}=\dfrac{54}{64}\\\\=0.8437[/tex]
In percentage rate of change,
[tex]\dfrac{f'(t)}{f(t)}=0.8437\times 100\\\\=84.37\%[/tex]
Hence, the required percent change is 84.37 %.
