Question

Let f(t) give the area in square miles of a town in year t, and g(t) the area in square kilometers. Find a formula for g by scaling the output of f. Use the fact that 1 mile equals 1.609 kilometers. You may enter the function f(t) verbatim, as you would for any other named function.

a) g(t)=−3.218t+1.609
b) g(t)=−2t+1
c) g(t)=−1.609t+1
d) g(t)=−2.5t+2.5

Answer 1

To convert the area from square miles to square kilometers, we multiply the output of f(t) by the conversion factor 2.59, as 1 square mile is approximately 2.59 square kilometers. None of the provided answer choices correctly scale f(t) by precisely 2.59, but option d is the closest with an incorrect scaling of 2.5.

Step-by-step explanation:

To find a formula for g(t), which gives the area in square kilometers, from f(t), the area in square miles, we need to use the conversion factor between square miles and square kilometers. Since 1 mile equals 1.609 kilometers, 1 square mile equals 1.609 squared, which is approximately 2.59 square kilometers (since 1.6092 is roughly 2.59).

Therefore, to convert f(t) from square miles to square kilometers, we multiply f(t) by 2.59. Thus, the correct formula for g(t) is obtained by multiplying the output of f(t) by 2.59.

Since none of the given options in the question exactly scale the output of f(t) by 2.59, there seems to be an error. However, the closest to the correct scaling factor is option d, which incorrectly uses 2.5 instead of the accurate conversion factor 2.59.