What is the annual rate of increase for a gallon of milk?

In summary, the price of milk increased from $1.79 to $2.15 over a two-year period, resulting in a rate of increase of $0.18 per year. However, the specific percentage increase per year cannot be determined without knowing the compounding period.
  • #1
mustang
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A gallon of milk was $1.79 two years ago. Today, it's $2.15. Find the rate it increased each year. :smile:
 
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  • #2
PLEASE do not double post! If this really is homework, then it shouldn't be posted under "general mathematics" and if it is not it shouldn't be posted here!

The price of milk, according to this problem increased from $1.79 to $2.15, an increase of ($2.15-1.79)= $0.36. Since that occurred over two years, the rate of increase is ($0.36)/(2 years)= $0.18 per year.
 
  • #3
I don't think that's what he's looking for. I think he wants a percentage per year. c is initial cost, C is final cost, r is rate, n is how many times (years?)

[tex]C = (c)(r)^n[/tex]

[tex]\frac{C}{c} = (r)^n[/tex]

[tex]^n\sqrt{\frac{C}{c}} = r[/tex]

[tex]r = 1.095955[/tex]

After the first year, the price of milk will be 1.96176 which is a change of 0.17176.
After the second year, the price of milk is 2.15 which is a change of 0.18824
 
  • #4
There is no way to tell. For all you know, the price could have gone up to $2.15 the first day. From the info given, I would of course not assume that. Apparently ShawnD is assuming the rate to be compounded once per year. The answer would be different for the arguably equally valid assumption that it is compounded continuously. I suppose you could declare your assumption, but make sure that you are not required to use a different compounding period.
 

1. What is the rate of increase problem?

The rate of increase problem is a mathematical concept that involves determining the rate at which a quantity is increasing over a certain period of time. It is commonly used in various fields such as finance, economics, and population studies.

2. How is the rate of increase calculated?

The rate of increase is calculated by dividing the change in the quantity by the initial quantity and then multiplying by 100 to express it as a percentage. The formula is: (final amount - initial amount) / initial amount * 100.

3. What factors can affect the rate of increase?

The rate of increase can be affected by various factors, such as the initial quantity, the time period, and any external influences or interventions. It can also be affected by the type of growth, whether it is linear or exponential.

4. How is the rate of increase problem used in real life?

The rate of increase problem is used in many real-life scenarios, such as predicting population growth, calculating compound interest in finance, and analyzing economic trends. It is also used in fields like epidemiology to track the spread of diseases.

5. What are some strategies for solving rate of increase problems?

Some strategies for solving rate of increase problems include identifying the initial quantity and final quantity, determining the time period, and using the appropriate formula. It is also helpful to understand the type of growth and any external factors that may be influencing the rate of increase.

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