The function for the value is:
[tex]V(t)=1.50\cdot(1.17)^t[/tex]
The annual growth rate is the increase in value for a year t to a year t+1, so we can find this rate by calculating the quotient [V(t+1)-V(t)] / V(t).
[V(t+1)-V(t)] represents the increase in value as the difference between the value in each year, and V(t) makes it to be relative to the year of reference.
[tex]\begin{gathered} \frac{V(t+1)-V(t)}{V(t)}=\frac{V(t+1)}{V(t)}-\frac{V\mleft(t\mright)}{V(t)}=\frac{V(t+1)}{V(t)}-1 \\ \\ \frac{V(t+1)}{V(t)}-1=\frac{1.50\cdot1.17^{t+1}}{1.50\cdot1.17^t}-1=1.17^{t+1-t}-1=1.17^1-1=0.17 \end{gathered}[/tex]
The annual growth rate is 0.17 or 17%.
The year 2025 is 25 years from 2000 so the value of t is t=2025-2000=25.
We can then calculate the value for V(25) as:
[tex]\begin{gathered} V(25)=1.50\cdot1.17^{25}\approx1.50\cdot50.66 \\ V(25)\approx75.99 \end{gathered}[/tex]
Answer:
The comic book will be worth $ 75.99 in the year 2025.
The annual growth rate of the comic book is 17%.
