Question

An invasive species has an initial population of 20 organisms. In five years it’s population has grown to 130. Assuming exponential growth, how many years will it take its population to reach 5,000?

Answer 1

The 15 years it will take its population to reach 5,000 if  initial population of 20 organisms.

What is an exponential function?

It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent $\rm y = a^x$

where a is a constant and a>1

Let's assume the exponential growth is:

$\rm y = Ae^{rt}$

From the problem:

$\rm 130 = 20e^{5r}$

$\rm e^{5r}= 6.5$

Taking ln both side:

We get:

r = 0.374

$\rm 5000 = 20e^{0.374t}$

After solving, we get:

t = 14.76 ≈ 15 years

Thus, the 15 years it will take its population to reach 5,000 if  initial population of 20 organisms.

Learn more about the exponential function here:

brainly.com/question/11487261

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