Answer:
The value of a is 7.
The value of b is 3.
Step-by-step explanation:
We are given the following function:
[tex]f(x) = ab^{x}[/tex]
Point (0,7)
This means that when [tex]x = 0, f(x) = 7[/tex]. So
[tex]f(x) = ab^{x}[/tex]
[tex]7 = ab^{0}[/tex]
[tex]a = 7[/tex]
So
[tex]f(x) = 7b^{x}[/tex]
(3, 189)
This means that when [tex]x = 3, f(x) = 189[/tex]. We use this to find b. So
[tex]f(x) = 7b^{x}[/tex]
[tex]189 = 7b^{3}[/tex]
[tex]b^3 = \frac{189}{7}[/tex]
[tex]b^3 = 27[/tex]
[tex]b = \sqrt[3]{27}[/tex]
[tex]b = 3[/tex]
The value of b is 3.
