SOLUTION: The consumer price index compares the costs of goods and services over various years, where 1967 is used as a base. The same goods and services that cost $100 in 1967 cost $42 in 1
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-> SOLUTION: The consumer price index compares the costs of goods and services over various years, where 1967 is used as a base. The same goods and services that cost $100 in 1967 cost $42 in 1
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Question 1200299: The consumer price index compares the costs of goods and services over various years, where 1967 is used as a base. The same goods and services that cost $100 in 1967 cost $42 in 1940. Assuming the exponential-decay model
(a) Estimate what the goods and services that cost $100 in 1967 cost in 1900. Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! the general expnential growth formula is f = p * (1+r)^n
f is the future value
p is the present value
(1+r) is the growth factor per time period.
r is the growth rate per time period.
in this formula:
f is the value in 1967
p is the value in 1940
n is equal to 1967 - 1940 = 27
formula becomes 100 = 42 * (1+r)^27
solve for (1+r) to get (1+r) = (100/42)^(1/27) = 1.032651381.
that's your growth factor per year.
that same growth factor per year applies to all years.
when you want to know what the value was in 1900, the equation becomes:
100 = p * 1.032651381 ^ 67
solve for p to get:
p = 100 / 1.032651381 ^ 67 = 11.61716321.
that's the value of goods and services in 1900, based on the equation.
i don't know what formula you were given, so i'm at a loss to apply your fromula to get the answer, but the answer should be the same regardless if you used my formula or the formula you were given.
the formula i used can be graphed as shown below.
the formula in the graph is y = 100 / 1.032651381 ^ x
this is derived from f = p * (1+r)^n, where we solve for p to get:
p = f / (1+r)^n
in the graph, p is replaced by y and n is replaced by x and f is replaced by 100 to get:
y = 100 / 1.032651381 ^ x
since i don't know what formula you were working from, i couldn't explain in that context.
if you can provide me with the formula you were working from, i can work the problem using that formula.
the answer should be the same.
