Question

nicholas sent a chain letter to his friends, asking them to forward the letter to more friends. every 12 weeks, the number of people who receive the email increases by an additional 99%, and can be modeled by a function, p, which depends on the amount of time, t (in weeks). nicholas initially sent the chain letter to 50 friends. write a function that models the number of people who receive the email t weeks since nicholas initially sent the chain letter. p(t) =

Explanation:

Step1: Identify initial value

The initial number of people who received the email is $P_0 = 50$.

Step2: Determine growth factor

A 99% increase means the growth factor per 12 weeks is $1 + 0.99 = 1.99$.

Step3: Define periodic growth rate

Since the growth occurs every 12 weeks, the number of 12-week periods in $t$ weeks is $\frac{t}{12}$.

Step4: Build exponential function

Combine initial value, growth factor, and periodic rate into the exponential model.
$P(t) = 50 \times (1.99)^{\frac{t}{12}}$

Answer:

$P(t) = 50(1.99)^{\frac{t}{12}}$