Question

What is the percent decrease modeled in the function, f(x)=0.45(0.91)^x?

55%

45%

9%

91%

Answer 1

\(\large\color{slate}{ f(x)=0.45(0.91)^x }\)
that means that you multiply times \(\large\color{slate}{ 0.91 }\) each time, correct?

Answer 2

Yes

Answer 3

multiplying times \(\large\color{slate}{ 0.91 }\) means that you are taking \(\large\color{slate}{ 91\text{%} }\) of what you previously had.
When you take \(\large\color{slate}{ 91\text{%} }\), that means that you leave out the other \(\large\color{slate}{ 9\text{%} }\)...

Answer 4

does that make sense?

Answer 5

Yes it does but why exactly does it have to be 91%?

Answer 6

What about the 0.45?

Answer 7

well, because multiplying times \(\large\color{slate}{ 0.91 }\) is same as taking \(\large\color{slate}{ 91\text{%} }\).

conversion from numbers to percent
\(\large\color{slate}{ \color{teal}{0.91}=(0.91\times 100)\text{%} =\color{teal}{91\text{%}} }\)
\(\large\color{slate}{ \color{teal}{0.44}=(0.44\times 100)\text{%} =\color{teal}{44\text{%}} }\)
\(\large\color{slate}{ \color{teal}{0.03}=(0.03\times 100)\text{%} =\color{teal}{3\text{%}} }\)

Answer 8

what do you mean what about 0.45?

Answer 9

0.45(0.91)^x
so does that 0.45 mean nothing?

Answer 10

that is just the coefficient, because, for any function:
\(\large\color{slate}{ y=a(b)^x}\)

when \(\large\color{slate}{ x=2}\), then \(\large\color{slate}{ y=a \times (b^2)}\)
when \(\large\color{slate}{ x=3}\), then \(\large\color{slate}{ y=a \times (b^3)}\)
when \(\large\color{slate}{ x=4}\), then \(\large\color{slate}{ y=a \times (b^4)}\)

and on...

Answer 11

so, \(\large\color{slate}{ 0.45(0.91)^x}\) would mean that as you add 1 to the X, you multiply another time by 0.91

Answer 12

What is the percent increase modeled in the function f(x)=20(1.5)^x ?
what about the increase?

Answer 13

can you convert 1.5 into the percent for me?

Answer 14

(multiply times 100, as I did before in 3 of my examples)

Answer 15

the percentage is 150%

Answer 16

yes

Answer 17

1.5 is same as 150 percent.

Answer 18

even if I am typing don't be afraid to interrupt me, by posting anything....

Answer 19

so \(\large\color{slate}{ 150\text{%} }\) is how much percent more than \(\large\color{slate}{ 100\text{%} }\) ?

Answer 20

Alright, I am really confused and would be 50%

Answer 21

yes, that would be 50%.

Answer 22

that means that you have a so \(\large\color{slate}{ 50\text{%} }\) increase in your case.

Answer 23

so \(\large\color{slate}{ 100\text{%} }\) is the entire thing.
when you take so \(\large\color{slate}{ 150\text{%} }\) you are taking an additional so \(\large\color{slate}{ 50\text{%} }\) on that.

Answer 24

I am starting to understand that now somethings that confuse me is the graph here it is http://prntscr.com/5ng1tr

Answer 25

okay, if you flipped the blue graph (I mean reflected across the x axis), would it be an exponential increase, or an exponential decay?

Answer 26

increase

Answer 27

yes. And when you flip this exponential increase, you are doing it by adding a - to it, because you will have all of the same outputs (y values) as the exponential increase function, except that they all will be negative.

Answer 28

which of the options given, is a normal exponential increase function, THAT IS REFLECTED ACROSS THE X AXIS, by adding a minus to the coefficient?

Answer 29

lost?

Answer 30

Yes kinda.

Answer 31

okay, lets consider this:


the left side picture describes the right side picture describes
\(\large\color{slate}{ y=a(b)^x }\) (when b>1) \(\large\color{slate}{ y=-a(b)^x }\) (when b>1)