Question

tobias sent a chain letter to his friends, asking them to forward the letter to more friends. the number of people who receive the email increases by a factor of 4 every 0.1 weeks, and can be modeled by a function, p, which depends on the amount of time, t (in weeks).
tobias initially sent the chain letter to 37 friends.
write a function that models the number of people who receive the email t weeks since tobias initially sent the chain letter.
p(t) =

Explanation:

Step1: Recall exponential growth formula

The general exponential growth function is $P(t) = P_0 \cdot r^{\frac{t}{k}}$, where $P_0$ is the initial amount, $r$ is the growth factor per period $k$.

Step2: Identify given values

$P_0 = 37$, $r = 4$, $k = 0.1$

Step3: Substitute values into formula

$P(t) = 37 \cdot 4^{\frac{t}{0.1}}$
Simplify the exponent: $\frac{t}{0.1} = 10t$, so $P(t) = 37 \cdot 4^{10t}$

Answer:

$37 \cdot 4^{10t}$