Question

The price of a gallon of milk has been rising about 1.36% per year since 2000. If milk costs $4.70 now what will it cost next year? If milk costs $4.70 now how long will it take for the price to top 5$?

Answer 1

Answer:

$4.76 for next year

5.5 years required to reach top of $5 or 6th year from now to top $5

Step-by-step explanation:

For first question,

initial price is $4.7

Now for formula of percentage, we have to find 1.36% of 4.7

Consider this 1.36% value as x

So, (x/4.7)x100 = 1.36

x = (1.36x4.7)/100

x = 0.063

Now, this x is the increment in previous price,

So, new price = 4.7 + x

New price = 4.7 + 0.063

                  = $4.763

For second question, we will use geometric series concept

In geometric series, their is a common ratio, which is ratio of two consecutive terms,

Since, every time increment in price is 1.36%, so this 1.36% is a common ratio

Formula for geometric series is

T(n) = ar^(n-1)

Now, T(n) is the term to be found or last term which is here $5

a is first term which is $4.7

r is common ratio which is 1.36% or 1.0136 to eliminate % sign

n is to be found

5 = (4.7) (1.0136)^(n-1)

5/4.7 = (1.0136)^(n-1)

Applying log on both sides

log (5/4.7) = log (1.0136)^(n-1)

0.026 = (n-1)log(1.0136)

0.026 = (n-1) * (5.86x10^-3)

n-1 = 4.43

n = 5.4 years

So, in 5.4 years, price will hit $5

So, 5.5 years price will top $5