Problema Solution
1. Write an exponential function to model the situation. Then predict the value of the function after 5 years (to the nearest whole number).
A population of 450 animals that decreases at an annual rate of 19%.
Answer provided by our tutors
The population decreases 18% during the first year,
so at the end of the first year 82% of 470 remain.
82% means 82 ÷ 100 = 0.82
so at the end of the first year 470(0.82) remain.
That number decreases 18% during the second year,
so at the end of the second year 82% of 470(0.82) remain.
82% of 470(0.82) is 470(0.82)(0.82) = 470(0.82)²
That number decreases 18% during the third year,
so at the end of the third year 82% of 470(0.82)² remain.
82% of 470(0.82)² is 470(0.82)²(0.82) = 470(0.82)³
Continuing this way, you can see at the end of five years
470(0.82)^5 = 174 (nearest whole number) remain,
and the general model for _x_ years is 470(0.82)^x