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The function below shows the number of students of a school who enrolled for ballet classes. Let f(x) represent the total number of students who enrolled for the classes after x years: f(x) = 12(1.06)x The average rate of change in the number of students who enrolled for ballet classes from the third to the fifth year is ________students per year.
@ganeshie8 @phi @mathmate
can you double check if there are any typoes in the function i think the "x" should be in the exponent
f(x) = 12(1.06)^x
Okay great! i hope you see the difference between \(12(1.06)x\) and \(12(1.06)^x\)
they are not same
tbh, no. This chapter made 0 sense to me at all.
don't wry, you will get it eventually if u persist
"average rate of change" is same as the "slope"
read the problem again, what exactly are we asked to find ?
Is this how you do the graph to find the difference? f(x) = 12(1.06)^x 1 12.72 2 13.47
you need to find the points when x = 3 and x = 5 not when x = 1 and x = 2
f(x) = 12(1.06)^x f(3) = 12(1.06)^3 = ?
but is that how i do it? 1 12.72 2 13.48 3 14.29 4 15.14 5 16.05
okay, look at the highlighted points 1 12.72 2 13.48 `3 14.29` 4 15.14 `5 16.05`
we need only them because we're asked to find the average rate of change between years 3 and 5
find the slope of those two points and you're done!
remember the slope formula ?
so i would do mean to find the difference? 14.29+15.14+16.05=45.48 45.48/3= 15.16 difference?
(3, 14.29) and (5, 16.05) slope = (16.05 - 14.29) / (5-3) = ?
Looks good! 0.88 is the average rate of change between years 3 and 5
ok cool! 1 more?
thank you for your help by the way!