# The function f(x) = 200 × (1.098)^x represents a village's population while it is growing at the rate of 9.8% per year. How do you create a table to show the village's population at 0, 2, 4, 6, 8, and 10 years from now?

Jul 9, 2018

Initial population is $200$ and population after $2 , 4 , 6 , 8 , \mathmr{and} 10$ years are $241 , 291 , 350 , 423 \mathmr{and} 509$ respectively.

#### Explanation:

Population function of village is f(x)=200(1.098)^x ; x

represents the number of year after now. .

Initial population: $x = 0 \therefore f \left(x\right) = 200 {\left(1.098\right)}^{0} = 200$

Population after $2$ years : $x = 2 \therefore f \left(2\right) = 200 {\left(1.098\right)}^{2} \approx 241$

Population after $4$ years : $x = 4 \therefore f \left(4\right) = 200 {\left(1.098\right)}^{4} \approx 291$

Population after $6$ years : $x = 6 \therefore f \left(6\right) = 200 {\left(1.098\right)}^{6} \approx 350$

Population after $8$ years : $x = 8 \therefore f \left(8\right) = 200 {\left(1.098\right)}^{8} \approx 423$

Population after $10$ years : $x = 10 \therefore f \left(10\right) = 200 {\left(1.098\right)}^{10} = 509$

Initial population is $200$and population after $2 , 4 , 6 , 8 , \mathmr{and} 10$

years are $241 , 291 , 350 , 423 \mathmr{and} 509$ [Ans]