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 \(V(t)=ab^t\).

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

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

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 ：\(\boxed{V(t)=17340(0.85)^t}\) is the equivalent function of the form \(V(t)=ab^t\).