Question

An exponential function may have a coefficient. In these cases, the equation is often written as...

Answer 1

It's all yours @BABYShawol184

Answer 2

Well by the equation
\[f(x) = ab ^{x}\]
We know that if x = 0 then b is one Therefore a is 54

Answer 3

Now we are given f(2)=6 so because we know what "a" is we can plug our values in

Answer 4

So...
\[f(2) = 54b ^{2}\]
Does that make sense?

Answer 5

yeah, somewhat

Answer 6

see, I knew you're good

Answer 7

Anyway...
Because f(2) = 6 we can put that into our equation
\[6=54b ^{2}\]
Are you still confused?

Answer 8

@Luis_Rivera Thank you :)

Answer 9

:)

Answer 10

no im following you now

Answer 11

So you're on track?

Answer 12

Yeah, i think so :P

Answer 13

Ok good stay with me :)
Now we would like to isolate to solve for b so we will divide each side by 54
\[\frac{ 6 }{ 54 } = b ^{2}\]

Answer 14

Are we still on tarck?

Answer 15

*track

Answer 16

yes.

Answer 17

Good :)

Answer 18

Now we square root both sides to get b.
To make it easier you can simply plug in 6/54 in our calculator and square root it and that's your answer for b. What did you get?

Answer 19

b= 1/3

Answer 20

CORRECT!!!! :) Good Job

Answer 21

so how do i find f(-3)?

Answer 22

So our equation is...
\[f(x) = 54(\frac{ 1 }{ 3 })^{x}\]

Answer 23

So we simply plug in -3 for x so it would be...
\[f(-3) = 54(\frac{ 1 }{ 3 })^{-3}\]
The power is (-3)

Answer 24

so it would be f(-3)=1458?

Answer 25

PERFECT!!! :) You're REALLY good at this!!

Answer 26

haha, im not, you are! can you help me with another? My teacher before spring break said, "I'll email you a few quizzes to take over break. Have them done before monday." This morning she emails us 10 quizzes. >.>

Answer 27

to make it worse.. on things we never learned.