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A city has a population of 737,000. The population $y$y​ increases by 2% each year.

a. Write an exponential function that represents the population after t years.

b. What will the population be after 14 years? Round your answer to the nearest thousand.

User Letin
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1 Answer

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a. Let's start by defining the initial population $P_0$ as 737,000, and the annual growth rate $r$ as 2% or 0.02. Then, the exponential function that represents the population after $t$ years can be written as:

$$y = P_0 (1 + r)^t$$

Substituting the values, we get:

$$y = 737{,}000(1 + 0.02)^t$$

Simplifying this expression, we get:

$$y = 737{,}000(1.02)^t$$

b. To find the population after 14 years, we can simply substitute $t=14$ into the exponential function we derived in part (a):

$$y = 737{,}000(1.02)^{14} \approx 1{,}064{,}535$$

Rounding to the nearest thousand, we get:

$$y \approx 1{,}064{,}000$$

Therefore, the population of the city after 14 years is estimated to be about 1,064,000.

User GvS
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