Question

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

Answer 1

Answer:

2 bears in 2020.

Step-by-step 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

$20\%=\frac{20}{100}=0.20$    

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.