Question

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?

Answer 1

Answer:

23040 bats

Step-by-step explanation:

Let N(t) be the number of bats at time

We know that exponential function

$y = ab$

According to question

$N(t) = ab^{2}$

Where t (in years)

Substitute t=2 and N(2)=180

$180 = ab^{2}$

Substitute t=5 and N(5)=1440

$1440 = ab^{5}$

Equation (1) divided by equation (2)

$\frac{180}{1440} = \frac{ab^{2} }{ab^{5}} = \frac{1}{b\frac{5-2}{}}$

By using the property

Substitute the values of b in equation (1)

Substitute t=9

Hence, after 9 years the expected bats in the colony=23040 bats