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:
[tex]y=a\cdot (1-r)^x[/tex], where,
y = Final quantity,
a = Initial value,
r = Decay rate in decimal form,
x = Time
[tex]20\%=\frac{20}{100}=0.20[/tex]
Upon substituting our given values in above formula, we will get:
[tex]y=150(1-0.20)^x[/tex]
[tex]y=150(0.80)^x[/tex], where x corresponds to year 2000.
To find the population in 2020, we will substitute [tex]x=20[/tex] in our equation as:
[tex]y=150(0.80)^{20}[/tex]
[tex]y=150(0.011529215046)[/tex]
[tex]y=1.7293822569[/tex]
[tex]y\approx 2[/tex]
Therefore, 2 bears are there predicted to be in 2020.
Since population is decreasing so population is best described as exponential decay.
