Find an expression of the form r^m, where r is approximately the monthly growth factor and m is the number of months.
A
270 frogs
B
1.017^m
Practice makes perfect
We can model the population of frogs by using the exponential growth function.
P(t)= a(1+ r)^tThe function can be used to find the population of frogs P(t) after t years, where a is the initial number of frogs and r is the percent rate of change.We know the initial number of frogs and the percent rate of change, which are 100 and 22 %. Then, a= 100 and r= 0.22.
P(t)= 100(1+ 0.22)^t ⇔ P(t)=100(1.22)^t
Now that we have the function, we can find the number of frogs in 5 years by substituting 5 for t.
The function P(t)=100(1.22)^t represents the yearly increase where t is the number of years. To write an expression representing equivalent monthly increase rate, we will use the fact that there are 12* t months in t years.
Let's start by rewriting the exponent as 12t12.
Now let 12t= m. Then, we have
(1.017)^(12t) ⇔ (1.017)^m
We have found an expression of the form r^m, where r is approximately the monthly growth factor and m is the number of months.
