Question
() Watch Video

The value of a car that depreciates over time can be modeled by the function $V(t)=24000(0.85{)}^{t+2}$. Write an equivalent function of the form $V(t)=a{b}^t$.
Answer Attempt 2 out of 2
$$V(t)=00(\mathrm{ab}{)}^t\text{ Submit Answer }$$

Step 1 ：The given function is $V(t)=24000(0.85{)}^{t+2}$. We are asked to rewrite this function in the form $V(t)=a{b}^t$.

Step 2 ：To do this, we can use the properties of exponents, specifically the rule that states $a^{m+n}=a^m\ast a^n$.

Step 3 ：Applying this rule, we can rewrite $(0.85{)}^{t+2}$ as $(0.85{)}^t\ast (0.85{)}^2$.

Step 4 ：Then, we calculate the value of $(0.85{)}^2$ and multiply it with 24000 to get the value of $a$. The base $b$ will remain as 0.85.

Step 5 ：After calculating, we get $a=17339.999999999996$ and $b=0.85$.

Step 6 ：Rounding $a$ to the nearest whole number, we get $a=17340$.

Step 7 ：$\boxed{{\displaystyle V(t)=17340(0.85{)}^t}}$ is the equivalent function of the form $V(t)=a{b}^t$.