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Alex Ar [27]
3 years ago
12

The number of bats in a colony is growing exponentially. After 2 years, there were 180 bats. After 5 years, there were 1440 bats

. If the colony continues to grow at the same rate, how many bats are expected to be in the colony after 9 years
Mathematics
1 answer:
TEA [102]3 years ago
8 0

Answer:

23040 bats

Step-by-step explanation:

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

We know that exponential function

y=ab^t

According to question

N(t)=ab^t

Where t (in years)

Substitute t=2 and N(2)=180

180=ab^2...(1)

Substitute t=5 and N(5)=1440

1440=ab^5...(2)

Equation (1) divided by equation (2)

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

By using the property a^x\div a^y=a^{x-y}

\frac{1}{8}=\frac{1}{b^3}

b^3=8=2\times 2\times 2=2^3

b=2

Substitute the values of b in equation (1)

180=a(2)^2=4a

a=\frac{180}{4}=45

Substitute t=9

N(9)=45(2)^9=23040 bats

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

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