Digital SAT Math Practice Questions – Advanced : Units

D

To find the rate at which the area of the forest is increasing in square kilometers per decade, we first need to convert the rate from acres to square kilometers.

1. Convert acres to square miles:

There are 640 acres in 1 square mile. Therefore:
\[ 1 \text{ acre} = \frac{1}{640} \text{ square miles} \]

The forest is increasing at a rate of 1 acre per decade. Thus, the rate in square miles per decade is:
\[ \frac{1}{640} \text{ square miles per decade} \]

2. Convert square miles to square kilometers:

We know that \( 1 \text{ mile} = 1.60934 \text{ kilometers} \), so:
\[ 1 \text{ square mile} = (1.60934)^2 \text{ square kilometers} = 2.58999 \text{ square kilometers} \]

Using the approximation given in the problem, \( 1 \text{ mile} \approx 0.62 \text{ kilometers} \), thus:
\[ 1 \text{ square mile} \approx (0.62)^2 \text{ square kilometers} \approx 0.3844 \text{ square kilometers} \]

3. Calculate the rate in square kilometers per decade:

Now, convert the rate from square miles per decade to square kilometers per decade:
\[ \frac{1}{640} \text{ square miles per decade} \times 2.58999 \text{ square kilometers per square mile} \approx \frac{2.58999}{640} \text{ square kilometers per decade} \]

Calculate the above expression:
\[ \frac{2.58999}{640} \approx 0.0040469 \text{ square kilometers per decade} \]

Rounding to four decimal places, we get:
\[ 0.0041 \text{ square kilometers per decade} \]