Question

The number of bacteria in a lab experiment can be modeled by the function C(t) = 7100(5)t+2. Write an equivalent function of the form C(t)=abt

Answer 1

Explanation:

To write the given function C(t) = 7100(5)t+2 in the form C(t) = ab^t, we need to rewrite it with a base (b) and an exponent (t) as follows:

C(t) = 7100(5)t+2

First, let's rewrite 7100 as a product of two numbers, one of which is a power of 5:

7100 = 5^2 * 284

Now, we can rewrite the function as follows:

C(t) = (5^2 * 284)(5)t+2

Now, we can simplify it further by multiplying the coefficients:

C(t) = 5^(2 + 1) * 284 * t^2

C(t) = 5^(3) * 284t^2

So, the equivalent function in the form C(t) = ab^t is:

C(t) = 284 * 5^3 * t^2

C(t) = 284 * 125 * t^2

C(t) = 35,500t^2