Question

The population of Marshville is loosing 20% of their population of frogs per year. There are currently 900 frogs in Marshville. How many frogs will there be in 5 years?

Answer 1

295 frogs

Explanation:

The Population of Marshville is loosing 20% of their population of frogs per year.

This means the value of the next year is 80% of the previous year.

This is an example of a geometric series in which the common ratio =80%

The nth term of a geometric series is given as:

`U_n=ar^(n-1)`

Where a=First Term, r=Common Ratio, n=Number of Terms

In this case.

a=900, r=80%=0.8, n=6 (After 5 years)

`U_5=900*0.8^(6-1)\\=900*0.8^(5)=294.9 \approx 295`

In 5 years time, there will be 295 frogs in Marshville.

Answer 2

There will be 262 frogs in 5 years

Explanation:

The population of Marshville can be modeled by the following equation.

`P(t) = P(0)(1 - r)^(t)`

In which P(t) is the population after t years, P(0) is the initial population, and r is how much the population decreases by year.

In this problem, we have that:

`P(0) = 900, r = 0.2`

So

`P(t) = 800(0.8)^(t)`

How many frogs will there be in 5 years?

This is P(5)

`P(5) = 800(0.8)^(5) = 262`

There will be 262 frogs in 5 years