A population of 100 frogs has a growth rate of 1.25% each month. At this growth rate,

the function f (x) = 100 (1.25) * gives the population in x months. In how many months

will the population first reach 500?

Answer: 7.2 months

Step-by-step explanation:

Hi, to answer this question we have to substitute f (x) = 500 in the equation given:

f (x) = 100 (1.25) ^x

500 = 100 (1.25) ^x

Solving for x (number of months)

500/100 = 1.25^x

5 = 1.25^x

log 5 = log 1.25^x

log 5 = x (log 1.25)

log 5 / log 1.25 = x

x = 7.2 months

Feel free to ask for more if needed or if you did not understand something.