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

Answer:

There will be 262 frogs in 5 years

Step-by-step 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

Answer 2

Answer:

295 frogs

Step-by-step 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.