Answer: The annual growth rate in the value of the Wheaties box = 12%
The box worth $32.30 currently in the year 2021.
Step-by-step explanation:
Exponential growth function : [tex]y=a(1+r)^x[/tex] , where a = initial value, r= rate of growth , x= time (i)
Given: [tex]V(t) = 2.99(1.12)^t[/tex] , where V(t) = value of a commemorative box of Wheaties t years after its purchase in 2000.
It can written as
[tex]V(t) =2.99(1+0.12)^t[/tex]
Comparing above function with (i), we get r=0.12
The annual growth rate in the value of the Wheaties box = 12%
Now , For 2021 , t=2021-2000=21
[tex]V(21)=2.99(1.12)^{21}\approx32.30[/tex]
Hence, the box worth $32.30 currently in the year 2021.
