To fill the table just replace the values in the formula:
i) year 1990 ⇒ t = 0 ⇒ p = 6191 (1.04)⁰ = 6,191
ii) year 1995 ⇒ t = 5 ⇒ p = 6191 (1.04)⁵ = 7,532
iii) year 2000 ⇒ t = 10 ⇒ p = 6191 (1.04)¹⁰ = 9,164
iv) year 2005 ⇒ t = 15 ⇒ p = 6191 (1.04)¹⁵ = 11,150
v) year 2012 ⇒ t = 20 ⇒ p = 6191 (1.04)²⁰ = 13.565
Questions
1) Does the model represent exponential model or decay?
Once you have filled the table you can certify it is a exponential growth.
Always that the exponent is positive (here it is) the exponential is exponential growth.
2) What s the percent of increase/decrease each year.
It is 4% increase.
Realize that each year the population is multiplied by 1.04, so the percent increase is 100 × (1.04p - p ) / p = 100 × (1.04 - 1) = 100 × 0.04 = 4%
3) What is the population in 1990?
We already calculated it: 6,190 (remember t = 0 in 1990).
4) What would be the population be in the year 2020?
t = 2020 - 1990 = 30 ⇒ p = 6,190 (1.04)³⁰ = 20,077
5) When does the population double?.
Make p = 2 × 6,190 in the formula ⇒
2 × 6190 = 6190 (1.04)ˣ
(1.04)ˣ = 2 ⇒
x log(1.04) = log(2) ⇒
x = log(2) / log(1.04) = 17.7 → 18 (whole number for years)
⇒ year = 1990 + 18 = 2008
