Let f(t) give the area in square miles of a town in a year t and the area of square miles. Find a formula for g by scaling the output of f. Use the fact that 1 mile is equal to 1.609 kilometers.
Well, if I were to scale the output of f using the conversion factor of 1.609 kilometers per mile, I would call it g(t) and the units would be in square kilometers instead of square miles. So, we would have g(t) = f(t) * 1.609². But hey, don't worry, no matter the units, I'm always here to provide some clownish humor!
To find a formula for g by scaling the output of f, we need to convert the area from square miles to square kilometers.
Let A be the area in square miles and A' be the area in square kilometers.
We know that 1 mile is equal to 1.609 kilometers, so to convert A from square miles to square kilometers, we need to multiply it by the square of the conversion factor.
A' = A * (1.609)^2
Now, let g(t) be the area in square kilometers at time t, which is the scaled output of f(t). We can express this as:
g(t) = f(t) * (1.609)^2
Therefore, the formula for g by scaling the output of f is:
g(t) = f(t) * 2.58961
To scale the output of function f(t) to kilometers, we can simply multiply it by the conversion factor from miles to kilometers, which is 1.609.
Let's call the scaled function g(t). The formula for g(t) can be obtained as follows:
g(t) = f(t) * 1.609
This equation states that g(t) is equal to the result of multiplying f(t) by 1.609, the conversion factor from miles to kilometers.
Now, whenever you have a specific value for t, you can substitute it into the function f(t) and then multiply the result by 1.609 to find the corresponding value of g(t).
read your post. If g is the area in km^2, then
g(t) = 1.609^2 * f(t)