Question

Question #1:How do you solve for n:
1=10,000(0.97)^n-1

Question #2: n=1 t(n)=3906.25
n=2 t(n)= 3125
n=3 t(n)= 2500
n=4 t(n)= 2000
n=5 t(n)= 1600

The rule is t(n)=2000(0.8)^n-4 Is this correct?

Answer 1

#1 Judging by the solution to #2, I'm assuming you meant

1 = 10,000 (0.97)^(n-1)
1/10000 = 0.96^(n-1)
-4ln10 = (n-1)ln0.97
n-1 = -4ln10/ln0.97
n = 1 - 4ln10/ln0.97

#2
0.8^0 = 1. so
n=4 t(n)=2000 fits

0.8^1 = 0.8, so t(5) = 1600 fits

I assume the rest do as well, so your solution looks good. Since there's not much formatting available her, you should write it as

t(n) = 2000(0.8)^(n-4) so there's no ambiguity.