Question

the number of views on a viral video can be modeled by the function $d(t) = 8400(2)^{t + 2}$. write an equivalent function of the form $d(t) = ab^t$.

Explanation:

Step1: Use the exponent rule \(a^{m+n}=a^m\times a^n\)

We have \(D(t) = 8400(2)^{t + 2}\), by the rule \(a^{m + n}=a^m\times a^n\), we can rewrite \((2)^{t+2}\) as \((2)^t\times(2)^2\). So \(D(t)=8400\times(2)^t\times(2)^2\).

Step2: Calculate \((2)^2\)

We know that \((2)^2 = 4\). Then substitute it back into the function: \(D(t)=8400\times4\times(2)^t\).

Step3: Multiply 8400 and 4

Calculate \(8400\times4 = 33600\). So the function becomes \(D(t)=33600(2)^t\).

Answer:

\(D(t) = 33600(2)^t\)