Question

Which of the following options results in a graph that shows exponential decay?
f(x) = 0.6(2)x
f(x) = 3(0.7)x
f(x) = 0.4(1.6)x
f(x) = 20(3)x

Answer 1

In general, the exponential function is \[\Large f(x) = a*b^x\] The base b determines if you have exponential growth or decay. If `0 < b < 1`, then you have exponential decay. If `b > 1`, then you have exponential growth.

Answer 2

For example, the function \[\Large f(x) = 33(2.7)^x\] has exponential growth because b = 2.7 is larger than 1.

Answer 3

Ok so for example f(x) = 3(0.7)to the x power is exponential decay @jim_thompson5910

Answer 4

correct

Answer 5

since b = 0.7 is between 0 and 1

ie it makes `0 < b < 1` true

Answer 6

Ok thank you

Answer 7

np

Answer 8

Hey wait can you help me solve another problem? @jim_thompson5910

Answer 9

sure

Answer 10

go ahead

Answer 11

For f(x) = 0.01(2)to the x power, find the average rate of change from x=2 to x=10

Answer 12

are you able to determine f(2) ?

Answer 13

Nope that's all the question says

Answer 14

replace every x with 2 and evaluate the function

Answer 15

These are the choices:
1.275
8
10.2
10.24

Answer 16

ignore the choices for now

Answer 17

\[\Large f(x) = 0.01(2)^x\]
\[\Large f(2) = 0.01(2)^2\]
\[\Large f(2) = ??\]

Answer 18

0.04

Answer 19

yes

Answer 20

now evaluate f(10)

Answer 21

Ok

Answer 22

I got 1,024

Answer 23

you should get something smaller than that, try again

Answer 24

\[\Large f(x) = 0.01(2)^x\]
\[\Large f(10) = 0.01(2)^{10}\]
\[\Large f(10) = ??\]

Answer 25

10.24

Answer 26

better

Answer 27

Is that right

Answer 28

Last step: compute
\[\Large \frac{f(b)-f(a)}{b-a}=\frac{f(10)-f(2)}{10-2} = ??\]

Answer 29

10.24 is not the answer, but it helps get you there

Answer 30

Wait is it 8over 8

Answer 31

\[\Large \frac{f(10)-f(2)}{10-2}=\frac{10.24-0.04}{10-2} = ??\]

Answer 32

Oh ok

Answer 33

So it 1.275

Answer 34

yes

Answer 35

And that's the right answer

Answer 36

yes

Answer 37

Ok thank you

Answer 38

np