11:04 Spiral Review \#5 Score: 0/2 Exponential Functions - Basic Question A town has a population of 17000 and grows at $$ 4 \% $$ every year. What will be the population after 12 years, to the nearest whole number? Answer Attempt 1 out of 2

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UpStudy AI · Accepted Answer

To find the population after 12 years, we can use the formula for exponential growth:

$$ P(t) = P_0 \times (1 + r)^t $$

where:
- $$ P(t) $$ is the population after $$ t $$ years,
- $$ P_0 $$ is the initial population,
- $$ r $$ is the annual growth rate as a decimal,
- $$ t $$ is the number of years.

Given:
- Initial population $$ P_0 = 17000 $$,
- Annual growth rate $$ r = 4\% = 0.04 $$,
- Number of years $$ t = 12 $$.

Substitute the given values into the formula:

$$ P(12) = 17000 \times (1 + 0.04)^{12} $$

Now, we can calculate the population after 12 years using the formula.
Calculate the value by following steps:
- step0: Calculate:
  $$17000\left(1+0.04\right)^{12}$$
- step1: Add the numbers:
  $$17000\times 1.04^{12}$$
- step2: Convert the expressions:
  $$17000\left(\frac{26}{25}\right)^{12}$$
- step3: Simplify:
  $$17000\times \frac{26^{12}}{25^{12}}$$
- step4: Rewrite the expression:
  $$125\times 136\times \frac{26^{12}}{25^{12}}$$
- step5: Rewrite the expression:
  $$5^{3}\times 136\times \frac{26^{12}}{5^{24}}$$
- step6: Reduce the numbers:
  $$136\times \frac{26^{12}}{5^{21}}$$
- step7: Multiply:
  $$\frac{136\times 26^{12}}{5^{21}}$$
The population after 12 years will be approximately 27217.547716. Rounding this to the nearest whole number, the population after 12 years will be approximately 27218.
The population after 12 years will be approximately 27,218.

11:04
Spiral Review #5
Score: 0/2
Exponential Functions - Basic
Question
A town has a population of 17000 and
grows at every year. What will be
the population after 12 years, to the
nearest whole number?
Answer
Attempt 1 out of 2

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11:04 Spiral Review #5 Score: 0/2 Exponential Functions - Basic Question A town has a population of 17000 and grows at every year. What will be the population after 12 years, to the nearest whole number? Answer Attempt 1 out of 2