Question

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?

Answer 1

Initial population is `200` and population after `2,4,6,8,and 10` years are `241,291,350,423 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 :.f(x)=200(1.098)^0 =200`

Population after `2` years : `x=2 :.f(2)=200(1.098)^2 ~~241`

Population after `4` years : `x=4 :.f(4)=200(1.098)^4 ~~291`

Population after `6` years : `x=6 :.f(6)=200(1.098)^6 ~~350`

Population after `8` years : `x=8 :.f(8)=200(1.098)^8 ~~423`

Population after `10` years : `x=10 :.f(10)=200(1.098)^10 =509`

Initial population is `200`and population after `2,4,6,8,and 10`

years are `241,291,350,423 and 509` [Ans]