The number of bats in a colony is growing exponentially. After 2 years, there were 120 bats. After 5 years, there were 960 bats. If the colony continues to grow at the same rate, how many bats are expected to be in the colony after 8 years?

7680 bats

Step-by-step explanation:

The number of bats in a colony is growing exponentially.

The formula for exponential growth =

y = ab^t

Where t = time in years

From the above question, we are told that:

After 2 years, there were 120 bats. After 5 years, there were 960 bats.

So we form an equation

120 = ab² Equation 1

960 = ab⁵ Equation 2

Hence:

120/960 = ab²/ab⁵

1/8 = b²/b⁵

1/8 = 1/ b^5 - 2

1/8 = 1/b³

1/2³ =1/ b³

2^-3 = b^-3

b = 2

We solve for a

120 = ab² Equation 1

120 = a × 2²

120 = 4a

a = 120/4

a = 30

If the colony continues to grow at the same rate, how many bats are expected to be in the colony after 8 years?

Using the formula

y = ab^t

t = 8

a = 30, b = 2

y = 30 × 2⁸

y = 7680 bats

none.

step-by-step explanation:

m

1

=

5

m1=5

b

=

−

1

b=-1

find the slope and y-intercept of the second equation.

tap for more

m

2

=

0

m2=0

b

=

−

6

b=-6

compare the slopes

m

m of the two equations.

m

1

=

5

,

m

2

=

0

m1=5,m2=0

compare the two slopes in the decimal form. if the slopes are equal, then the lines are parallel. if the slopes are not equal, then the lines are not parallel.

m

1

=

5

,

m

2

=

0

m1=5,m2=0