Question

It is estimated that t months from now, the population of a certain town will be changing at the rate of 4+ 5t^2/3 people per month. If the current population is 10,000, what will the population be 8 months from now?

Answer 1

Answer:

240000

Step-by-step explanation:

Represent the exponential equation.

$10000 (5 {t}^{ \frac{2}{3} } + 4) =$

Replace 8 with t

$10000(5(8) {}^{ \frac{2}{3} } + 4)$

$10000(5 \times 4 + 4)$

$10000(24) = 240000$

Answer 2

The population of the town after 8 month will be 2,40,000.

What is exponential growth?

Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function.

Let P be the population of the town after 8 months

According to the given question

The current population of the town = 10,000.

Also, the population of the town is changing at the rate of $4+5t^{\frac{2}{3} }$.

Therefore, the population of the town after 8 month is given by the exponential function

$P = 10000(4+5t^{\frac{2}{3} } )$

Substitute t =8 in the above equation

⇒$P = 10000(4 + 5(8)^{\frac{2}{3} } )$

⇒$P = 10000(4 + 5(2^{3}) ^{\frac{2}{3} } )$

⇒$P = 10000(4+5(4))$

⇒$P = 10000(24)$

⇒$P = 240000$

Hence, the population of the town after 8 month will be 2,40,000.

Find out more information about exponential growth here:

https://brainly.com/question/11487261

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