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The population of a town was 5655 in 2010. The population grows at a rate of 2.6% annually.
(a) Use the exponential growth model to write an equation
that estimates the population t years after 2010.
(b) Fill in the following table for each value of . Show your work. You may use a calculator to
calculate the final answer. Round your answers to the nearest whole number.

Sagot :

Raphealnwobiidn

The exponential equation used to represent the population of the town is given by y = 5655(1.026)ˣ

An exponential function is in the form:

y = abˣ

where y, x are variables, a is the initial value of y and b is the multiplier.

Let y represent the population remaining after x years.

The population grow at the rate of 2.6% annually. Hence:

b = 100% + 2.6% = 1.026

There are initially 5655 people, hence a = 5655.

The equation becomes:

y = 5655(1.026)ˣ

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