Question

I think it is C, am i right?
Which of the following options results in a graph that shows exponential growth?
f(x) = 0.4(0.2)x
f(x) = 4(0.98)x
f(x) = 0.7(5)x
f(x) = 5(4)−x

Answer 1

why C?

Answer 2

i really dont know, i think it is also B as well

Answer 3

Rule:
If you have \[\Large f(x) = a*(b)^x\] f(x) will have exponential growth if `b > 1` or f(x) will have exponential decay if `0 < b < 1`

Answer 4

so it is neither C or B..

Answer 5

Flip things around
If you have \[\Large f(x) = a*(b)^{-x}\] f(x) will have exponential decay if `b > 1` or f(x) will have exponential growth if `0 < b < 1`

Answer 6

which function has `b > 1` ? and has `x` (not `-x`) in the exponent?

Answer 7

it has to be A then

Answer 8

in choice A, what are the values of a and b?

Answer 9

8

Answer 10

for `f(x) = 0.4(0.2)^x`, the value of a and b are

a = 0.4
b = 0.2

agreed?

Answer 11

oh yes, im sorry i miss read what you said.

Answer 12

so b = 0.2

is b > 1 true?

Answer 13

i think it is

Answer 14

0.2 > 1 is true?

Answer 15

here is a graph to interactively play with

https://www.desmos.com/calculator/fhg9iipwt0

Answer 16

adjust the sliders for 'a' and 'b'. Make sure 'a' stays as a positive number

Answer 17

a stayed as a positive number @jim_thompson5910

Answer 18

yeah make a = 2 or something

then adjust the slider for b

Answer 19

they stayed positive @jim_thompson5910