To write the function \( D(t) = 3500(2)^{t+1} \) in the form \( D(t) = ab^t \), we need to manipulate the expression a bit.
Starting with:
\[ D(t) = 3500(2)^{t+1} \]
We can rewrite \( (2)^{t+1} \) as \( (2^t)(2^1) \):
\[ D(t) = 3500 \cdot (2^t) \cdot 2 \]
Now, simplifying it gives us:
\[ D(t) = 3500 \cdot 2 \cdot 2^t \]
Calculating \( 3500 \cdot 2 \) gives us:
\[ 3500 \cdot 2 = 7000 \]
So, we can rewrite the function as:
\[ D(t) = 7000 \cdot 2^t \]
Thus, in the form \( D(t) = ab^t \), we have:
- \( a = 7000 \)
- \( b = 2 \)
Therefore, the equivalent function is:
\[ D(t) = 7000 \cdot 2^t \]