Question

A population of 200 animals has a growth rate of 1.03% each year. at this growth rate, the function f(x)=200(1.03)^x gives the population in x years. in how many years will the population first reach 300? answer

Answer 1

For this case, the first thing we should do is use the following equation:
 f (x) = 200 (1.03) ^ x
 We substitute f (x) = 300:
 300 = 200 (1.03) ^ x
 We clear the value of x:
 log1.03 (300/200) = log1.03 ((1.03) ^ x)
 x = log1.03 (300/200)
 x = 13.72
 Answer: 
 the population will first reach 300 in about 13.72 years.