A gallon of milk that cost $3.89 a year ago now costs $4.05. A. If the cost is increasing linearly, what is the growth rate? If the cost kept increasing in the same way, what will the milk cost 5 years from now? B. If the cost is increasing exponentially, what is the growth rate? What will the milk cost in 5 years?

A) 1 = 0.16 = 16%

2) $4.69

B) 1 = 0.04 = 4%

2) $4.76

Step-by-step 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

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