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

Question

Rocket

Mathematics

23 July, 11:57

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

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Answers (1)

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Muffy · 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.