Given the following exponential function, identify whether the change
represents growth or decay, and determine the percentage rate of increase or
decrease
y = 740(1.5)
Growth
% increase
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82

  Given function is a growth function and the percentage rate of increase is 50%.

    Given function in the question,

If a function is given by,

y = Final value

I = Initial value

r = rate of increase or decrease

x = Duration

If 'r' is positive, function will be a growth function and for negative value of 'r', function will be a decay function.

Given function 'y' can be written as,

     Since, rate is positive, given function will be a growth function.

                And the rate of increase will be r = 50%

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Step-by-step explanation:

Exponential functions have the standard form

where a is the initial value and b is the growth/decay rate.  The rule is that the function is growth if the value for b is greater than 1; the function is decay if the value for b is greater than 0 but less than 1.  Our b value is 1.5, so this is a growth function.

The tricky part about the growth rate is determining what the percent increase is.  When you are dealing with a growth rate, you start with 100% of what you're dealing with, and are then adding to it the growth rate.  For example, if the initial population of bacteria in a dish is 10 and it increases at a rate of 5% per hour, then the rate of increase in the function would be the 100% of the population that we started with plus 5%, giving us a growth rate of 100% + 5% = 105%.  In decimal form that would be 1.05.

For us in our problem, we have the 100% of whatever to start with and added another 50% to that to give us a growth rate of 150%, or in decimal form, 1.5.  So the increase is 50%

look at the picture.

y-intercept for the function on a picture is 4 → point (0, 4).

y-intercept for the function

is for x = 0. substitute:

y-intercept is 8 → point (0, 8).

hello from mrbilldoesmath!

answer:   x^2 + y^2 = 1024

discussion:

the equation of a circle with center (h,k) and radius "r" is

(x-h)^2 + (y-k)^2 = r^2.

in our case

(x-0)^2 + (y-0) ^2 = 32^2 = 1024

you,

mrb