SOLUTION: A)Suppose f is an exponential function and f(0)=9 and f(1)=17. Write a function formula for f. B)Suppose g is an exponential function and g(2)=10 and g(3)=14. Write a function for

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A)Suppose f is an exponential function and f(0)=9 and f(1)=17. Write a function formula for f. B)Suppose g is an exponential function and g(2)=10 and g(3)=14. Write a function for      Log On


   

Question 1128856: A)Suppose f is an exponential function and f(0)=9 and f(1)=17. Write a function formula for f.
B)Suppose g is an exponential function and g(2)=10 and g(3)=14. Write a function formula for g.
Found 2 solutions by josmiceli, MathLover1:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
A)
+f%28x%29+=+a%2Ab%5Ex+
+f%280%29+=+9+
+9+=+a%2Ab%5E0+
+9+=+a+
---------------------
+f%281%29+=+17+
+17+=+9%2Ab%5E1+
+b+=+17%2F9+
----------------------------
+f%28x%29+=+9%2A%28+17%2F9+%29%5Ex+
----------------------------
B)
+g%28x%29+=+a%2Ab%5Ex+
+g%282%29+=+10+
+10+=+a%2Ab%5E2+
------------------------
+g%283%29+=+14+
+14+=+a%2Ab%5E3+
-------------------------
+14%2F10+=%28+a%2Ab%5E3%29+%2F+%28a%2Ab%5E2%29+
+1.4+=+b+
and
+10+=+a%2A%287%2F5%29%5E2+
+10+=+a%2A%28+49%2F25+%29+
+a+=+250%2F49+
+a+=+5.102+
------------------------------
+f%28x%29+=+5.102%2A1.4%5Ex+
------------------------------


Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

exponential formula is
f%28x%29=+ab%5Ex
if f%280%29=9 we have
9+=+ab%5E0
9+=+a%2A1
a=9
and if f%281%29=17
17+=+9b%5E1
b=%2817%2F9%29
so, your formula is:
f%28x%29+=+9%2817%2F9%29%5Ex

B)


g%28x%29+=+ab%5Ex.........if +g%282%29=10
if g%282%29=10
10+=+ab%5E2
a=10%2Fb%5E2............1)
if g%283%29=14
14+=+ab%5E3
a=14%2Fb%5E3............2)

from 1) and 2), we have
10%2Fb%5E2=14%2Fb%5E3
10b%5Ecross%283%29=14cross%28b%5E2%29
10b=14
b=14%2F10
b=7%2F5
go to
a=10%2Fb%5E2............1) substitute b
a=10%2F%287%2F5%29%5E2............1)
a=10%2F%2849%2F25%29
a=%2810%2A25%29%2F49
a=250%2F49

=> g%28x%29+=+%28250%2F49%29%287%2F5%29%5Ex