The number of bats in a colony is growing exponentially Afte

The number of bats in a colony is growing exponentially. After 1 year, there were 70 bats. After 4 years, there were 560 bats. If the colony continues to grow at the same rate, how many bats are expected to be in the colony after 7 years? Do not include units in your answer.

Solution

Solution

The number of bats in a colony is growing exponentially

Let P(t) = number of bat any time t in year

P(t) = P_o e^kt

Let Initially there were P₀ number of Bat

It is given that t = 1 . and P(1)= 70

70 = P₀ e^k

and t = 4 and P(4) = 560

therefore

560 = P₀ e^k4

Using both equation

e^3k = 8

k =0.693

Now using this value of P₀

P_o = 35

therefore

bats are expected to be in the colony after 7 years

P(7) = 35 e^0.693*7

^{= 4476}