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 9.1 weeks, and can be modeled by a function, f(p) which depends on the amount of time, t (in weeks). Tobias initially sent the chain letter to 37 friends.

Write an exponential function describing this scenario. Use "^" to denote an exponent and "/" to denote a fraction sign.


•THIS WAS FROM KHAN ACADEMY

•EXPONENTIAL MODELS IF THAT HELPS

Answer 1

f(p) = 37*4^(t/9.1)

Explanation:

The generic model for an exponencial function is:

P = Po*r^t

Where P is the final value, Po is the inicial value, r is the rate and t is the time.

In our case, the function if f(p), the inicial value is 37, the rate is 4 for every 9.1 weeks and the time is t, in weeks.

As the rate occurs for every 9.1 weeks, we need to use this equation:

P = Po*r^(t/9.1)

This way, when t = 9.1, the rate will occur one time (will be r^1)

So, our final equation is:

f(p) = 37*4^(t/9.1)