Answer:
A) 1 = 0.16 = 16%
2) $4.69
B) 1 = 0.04 = 4%
2) $4.76
Explanation:
A gallon of milk that cost $3.89 a year ago now costs $4.05.
A. Linear Growth rate formula:
P(t) = Po + rt
P(t) = Cost After t years = $4.05
Po = Initial cost = $3.89
1) If the cost is increasing linearly, what is the growth rate?
When t = 1
P(t) = Po + rt
4.05 = 3.89 + r × 1
r = 4.05 - 3.89
r = 0.16
Converting to percentage
= 0.16 × 100
= 16%
2) If the cost kept increasing in the same way, what will the milk cost 5 years from now?
P(t) = Po + rt
P(t) = 3.89 + 0.16 × 5
P(t) = 3.89 + 0.8
P(t) = 4.69
= $4.69
B. Exponential growth rate formula
P(t) = Po (1 + r)^t
If the cost is increasing exponentially, what is the growth rate?
1) when t = 1
P(t) = Cost After t years = $4.05
Po = Initial cost = $3.89
4.05 = 3.89 (1 + r)
Divide both sides by 3.89
4.05/3.89 = 3.89(1 + r)/3.89
1.0411311054 = 1 + r
r = 1.0411311054 - 1
r = 0.0411311054
Approximately = 0.04
Converting to Percentage
= 4%
2) What will the milk cost in 5 years?
P(t) = 3.89 (1 + r)^t
P(t) = 3.89 (1 + 0.0411311054)⁵
= $4.7585727225
Approximately = $4.76