Question

Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y=590(1.061)^x

Answer 1

Answer:

Determine if its a growth or decay.Then find the percent increase of decrease. 1.y=16(.25)^x 2.y=0.8(1.28)^x 3.y=17(1/5)^x''.

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Expert Answers info

HALA718 eNotes educator | CERTIFIED EDUCATOR

y= 16(0.25)^x

The exponential equation represents an exponential decay because the rate of decay is 0.25 which is less than 1.

The general form equation is:

y(x)= a(1-r)^x such that r is the decay percent.

Comparing two equation we have 1-r = 0.25

==> r= 1-0.25 = 0.75 = 75%

Then, the decay percent is 75%.

2. y= 0.8(1.8)^x

The equation represents exponential growth because the growth factor is greater than 1.

==> 1+r = 1.8

==> r= 0.8 = 80%

Then, the growth percent is 80%

3. y= 17(1/5)^x

The equation represents exponential decay because 1/5 is less than 1.

==> 1-r = 1/5

==> r= 1- 1/5 = 4/5 = 0.8= 80%

Then, the decay percent is 80%

Answer 2

The given exponential function will grow at 6.1%

Given,

y = $590(1.061)^x$

To find,

identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.

Solution,

We have,

y = $590(1.061)^x$

The equation represents exponential growth because the growth factor is greater than 1.

The general form equation is:

y(x)= a(1-r)^x such that r is the growth percent.

==> 1+r = 1.061

==> r = 0.061 = 6.1%

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