Bear Population

Question

The size of the bear population at a national park increases at the rate 4.3

of per year. If the size of the current population is 108, find how many bears there should be in 5 years. Use y= Yoe^0.043t and round to the nearest whole number.

Answer 1

I believe you meant "at the rate of 4.3% per year." The general formula for exponential growth is:

 

P(t) = P₀·(1+rate)^t/p

• P(t) = population at year t
• P₀ = starting population = 108
• rate = growth rate expressed as a decimal = 0.043
• t = years = 5
• p = period needed to grow at the expressed rate = 1 year

 

P(t) = P₀·(1+rate)^t/p

P(5) = 108·(1+0.043)^5/1

P(5) = 108·(1.043)⁵

 

Use your calculator to get the answer.  Round to the nearest whole number because we can't have part of a bear.