a function that model the number of people that receives email in week t is [tex]P(t)=37(4)^{\frac{t}{9.1}}[/tex] .
Step-by-step explanation:
Here we have , Tobias sent a chain letter to his friends . The number of people who receives the email increases by a factor of 4 in every 9.1 weeks , and can be modeled by a function P, which depends on the amount of time t weeks . Tobias initially sent letter to 37 friends . We need to write a function that model the number of people that receives email in week t . Let's find out:
Basically it's an exponential function as
[tex]f(x) = e^{ax}[/tex] , In question initial value is 37 & and for every 9.1 weeks there is increase in people by a factor of 4 i.e.
⇒ [tex]P(t)=37(4)^t[/tex]
But , wait ! People increase in every 9.1 weeks not every week so modified equation will be :
⇒ [tex]P(t)=37(4)^{\frac{t}{9.1}}[/tex]
Therefore , a function that model the number of people that receives email in week t is [tex]P(t)=37(4)^{\frac{t}{9.1}}[/tex] .
