Urgent *WILL MEDAL!*: Which function represents exponential growth?

y=9/7(2/3)^x

y=4/5(4/5)^x

y=2.3(3/2)^x

y=4.1(5/6)^x

Thanks! :)

Question

Urgent *WILL MEDAL!*: Which function represents exponential growth?

y=9/7(2/3)^x

y=4/5(4/5)^x

y=2.3(3/2)^x

y=4.1(5/6)^x

Thanks! :)

jim_thompson5910 · Answer

Rule:

$$\Large y = a*b^x$$
has exponential growth only if b > 1

jim_thompson5910 · Answer

For example,

$$\Large y = 2*1.7^x$$
represents growth because b = 1.7 which is larger than 1

butterflyhope · Answer

Ohhh I get it but none of them are greater than 1??

jim_thompson5910 · Answer

convert each of the fractions to decimal form

that should help

jim_thompson5910 · Answer

ex:

9/7 = 1.29
2/3 = 0.67

y=9/7(2/3)^x turns into y = 1.29*0.67^x

the base for x is 0.67 which is NOT greater than 1, so it is NOT a growth function. It's actually decaying

So A is out

butterflyhope · Answer

It's C because 3/2 = 1.5?

jim_thompson5910 · Answer

correct

butterflyhope · Answer

Thank you :)

jim_thompson5910 · Answer

1.5 = 1+r

solve for r to get r = 0.5

since r = 0.5 = 50%, we have 50% growth here

jim_thompson5910 · Answer

you're welcome