Question

: A new bear population that begins with 150 bears in 2000 decreases at a rate of 20% per year.

Challenge question: based on the function, how many bears are there predicted to be in 2020? Is the population best described as exponential growth or exponential decay? Justify your reasoning with evidence.

Answer 1

2 bears in 2020.

Explanation:

We have been given that a new bear population that begins with 150 bears in 2000 decreases at a rate of 20% per year.

We will use exponential decay formula to solve our given problem as:

`y=a\cdot (1-r)^x`, where,

y = Final quantity,

a = Initial value,

r = Decay rate in decimal form,

x = Time

`20\%=(20)/(100)=0.20`

Upon substituting our given values in above formula, we will get:

`y=150(1-0.20)^x`

`y=150(0.80)^x`, where x corresponds to year 2000.

To find the population in 2020, we will substitute
`x=20` in our equation as:

`y=150(0.80)^(20)`

`y=150(0.011529215046)`

`y=1.7293822569`

`y\approx 2`

Therefore, 2 bears are there predicted to be in 2020.

Since population is decreasing so population is best described as exponential decay.