Assessment of Exponential models (Algebra 1)

Question

There is 20 of these and since my teacher is busy helping other students out I was thinking I could get some help here. And it's due in a couple hours :/ Here is what I'm struggling with:

R(x) = 3(1.23)^x

Initial Value: Growth or Decay: When will this model reach 30?

Percent rate of change: Amount after 5 years:

(also " ^ " means the following is an exponent)

G(x) = 120(0.75)^x

Initial Value: Growth or Decay: When will this model reach 50?

Percent rate of change: Amount after 7 years:

Answer 1

If you have 102% (or 1.02) isn't that growth? It means you are adding 2% every time period.

If you have 98%(0.98), then you're LOSING 2% every time period.

30 = 3(1.23)^x

Well, thats 123%, so it's growth of 23%.

10 = 1.23^x

log(10) = xlog(1.23)

x = log(10)/log(1.23)

x = 11 years

3(1.23)⁵ = 8

The other is on you.

Answer 2

R(x) = 3(1.23)^x

0 3

1 3.75

2 4.5387

3 5.5826

There's no end to values. Keep substituting until you hit 30.