Answer:
68% increase every day
Step-by-step explanation:
Missing question: complete the following sentence:
Every day, there is a ....% addition to/removal from the number of people who receive the mail
The function that models the relationship between the elapsed time t (in days) and the number of people who receive the mail P(t) is:
[tex]P(t)=(1.09)^{6t+25.5}[/tex]
where
t is the elapsed time, in days
P(t) is the number of people who receive the mail
Here we want to find the rate of change of the function.
The rate of change of P(t) per every hour can be calculated by evaluating the ratio between P(t+1) and P(t):
[tex]r=\frac{P(t+1)}{P(t)}[/tex]
Substituting,
[tex]r=\frac{(1.09)^{6(t+1)+25.5}}{(1.09)^{6t+25.5}}=\\=\frac{(1.09)^{6t+6+25.5}}{(1.09)^{6t+25.5}}=\\=\frac{(1.09)^{6t+25.5}\cdot (1.09)^6}{(1.09)^{6t+25.5}}=(1.09)^6=1.68[/tex]
So, every day there is a 68% increase.
