Question

cameron sent a chain letter to his friends, asking them to forward the letter to more friends. the relationship between the elapsed time ( t ), in days, since cameron sent the letter, and the number of people, ( p(t) ), who receive the email is modeled by the following function: ( p(t) = 100 cdot (1.83)^{\frac{t}{2.5}} ) complete the following sentence about the rate of change in the number of people who receive the email. every (square) days, the number of people who receive the email increases by an additional 83%.

Explanation:

Step1: Identify growth factor condition

We need the exponent of 1.83 to equal 1, since a growth factor of 1.83 corresponds to an 83% increase.

Step2: Set up equation for exponent

$$\frac{t}{2.5} = 1$$

Step3: Solve for t

Multiply both sides by 2.5:
$$t = 1 \times 2.5 = 2.5$$

Answer:

2.5