SOLUTION: The consumer price index compares the cost of goods and services over various years. The same goods and services that cost $100 in 1967 cost $148.50 in 1977. Assuming exponential g

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Question 203504: The consumer price index compares the cost of goods and services over various years. The same goods and services that cost $100 in 1967 cost $148.50 in 1977. Assuming exponential growth, find the value of these same goods and services in 1999.

After what period of time did the same goods and services cost double that of 1967?
Hint: x.xx years
can someone help please

Answer by stanbon(48569) (Show Source):
You can put this solution on YOUR website!
The consumer price index compares the cost of goods and services over various years. The same goods and services that cost $100 in 1967 cost $148.50 in 1977. Assuming exponential growth, find the value of these same goods and services in 1999.
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Let x=0 correspond to the year 1967.
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Form::::::::: y = a*b^x
(0,100):::: 100 = a*b^0
(10,148.50):148.5= a*b^10
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1st equation says a = 100
Then b = 1.485^(1/10)
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So the equation is y = 100
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find the value of these same goods and services in 1999.
x = 1999-1967 = 32
y = 100*(1.485^(3.2) = $354.43
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After what period of time did the same goods and services cost double that of 1967?
200 = 100(1.485^(x/10))
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1.485^(x/10) = 2
(x/10)log(1.485) = log(2)
(x/10) = 1.753
x = 17.53 years
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Year: 1967 + 17.53 = 1969 when rounded up.
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Cheers,
Stan H.