a study of the annual population of toads in a county park shows the population, S(t), can be represented by the function S(t) = 152(1.045)^t, where the t represents the number of years since the study started. based on the function, what is the growth rate?

0.045 is the growth rate.

Step-by-step explanation:

A generic exponential growth function can be written as:

f(t) = A*(1 + r)^t

where A is the initial amount.

t is the unit of time.

r is the rate of growth.

For example if we have an increase of 10% per year, with an initial population of 100 we have that:

A = 100, r = 10%/100% = 0.10, t = number of years.

the equation will be:

f(t) = 100*(1 + 0.10)^t

Now, in this case the equation is:

S(t) = 152*(1.045)^t

We can write this as:

S(t) = 152*(1 + 0.045)^t

Then 152 is the initial amount and 0.045 is the growth rate.

b. 24 mm

step-by-step explanation:

use the pythagorean theorem.

a^2 + b^2 = c^2

a^2 + 7^2 = 25^2

a^2 + 49 = 625

a^2 = 576

a = 24

answer: b. 24 mm

x= 3^y

step-by-step explanation: