From 1970 to 1980, the consumer price index (CPI) increased from 38.8 to 82.4. If a dozen eggs cost [tex]$0.25[/tex] in 1970 and the price of eggs increased at the same rate as the CPI from 1970 to 1980, approximately how much did a dozen eggs cost in 1980?

A. [tex]$0.82[/tex]
B. [tex]$0.39[/tex]
C. [tex]$0.28[/tex]
D. [tex]$0.53[/tex]

To find out how much a dozen eggs cost in 1980 if the price increased at the same rate as the Consumer Price Index (CPI) from 1970 to 1980, follow these steps:

1. Determine the CPI Increase:
The CPI increased from 38.8 in 1970 to 82.4 in 1980. We need to calculate the rate of increase.

[tex]\[
\text{Rate of Increase} = \frac{\text{CPI in 1980}}{\text{CPI in 1970}} = \frac{82.4}{38.8}
\][/tex]

[tex]\[
\text{Rate of Increase} \approx 2.12
\][/tex]

2. Apply the Same Rate of Increase to the Egg Prices:
The cost of a dozen eggs in 1970 was [tex]$0.25. We use the same rate of increase to find the price in 1980.

\[
\text{Cost of Eggs in 1980} = 0.25 \times 2.12
\]

\[
\text{Cost of Eggs in 1980} \approx 0.53
\]

So, the cost of a dozen eggs in 1980 was approximately $[/tex]0.53. Therefore, the correct answer is:

D. $0.53