Answer:
The original function is f(m) = 5(1.07)^m, with the m as an exponent
part A) if the final length is 9.19, we can set f(m) = 9.19 and solve for m
plugging it into a calculator, I get m = ~8.99, so a bit less than 9. therefore, a reasonable domain might be all the m values 9 or below, or m ≤ 9
part B) the y-intercept of a function is the value of the independent variable when the dependent variable = 0. the two variables in your problem are height and number of months - which one do you think is the independent one, and which one is dependent? then re-interpret "value of the independent variable when the dependent variable = 0" in terms of the actual quantities that the variables represent
part C) average rate of change from m = 1 to m = 9
f(9)−f(1)9−1
evaluate, and think about what that represents in terms of height and number of months
5 minutes x minutes
--------------- = -------------
4 dishes 24 dishes
using cross products
5 * 24 = 4 * x
divide each side by 4
5*24/4 = x
30=x
It will take 30 minutes
They aren’t like terms became 5x^2y has an exponent
We could have the numbers
5x^2 and 5x and they wouldn’t be like terms because one has an exponent
