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?
Answers
Answer:
Step-by-step explanation:
Population function of village = f(x) = 200(1.098)x, representing the number of years after now -
x | f(x)=200(1.098^x)
0 | 200
2 | 241.1208 ≅ 241
4 | 290.6962 ≅ 291
6 | 350.4645 ≅ 350
8 | 422.5214 ≅ 423
10 | 509.3935 ≅ 509
When the population doubles it will be at 400
Thus, 400 = 200(1.098^x)
1.098^x = 2
Taking log on both the sides
log (1.098^x) = log 2
x[log 1.098] = log 2
x = (log 2)/(log 1.098)
x = 7.4141 years
Rounded to the nearest half a year the population will double in 7 1/2 years or 7.5 years
1. 0 2 4 6 8 10
200 241 290 350 423 509
2. on a graph I would mark the points above and connect them with a line, it would look like a straight line going up to the right on the positive axis for both x and y
3. so when the population becomes 2x more it would be at 400. I can show this as 400=200(1.098)^x. when solved, x=7.4 years, which can be rounded to 7.5 for the nearest 1/2 year.
the water well will need to be dug in 7 1/2 years.
i used the info from the other answer to write it out in simpler terms and in the format the question wanted. :)