Answer:
[tex]f(10)= 236196[/tex]
Step-by-step explanation:
Given
[tex](x,y) = (0,4)[/tex] --- y intercept
[tex]b = 3[/tex] --- growth factor
Required
[tex]f(10)[/tex]
An exponential function is represented as:
[tex]y = ab^x[/tex]
[tex](x,y) = (0,4)[/tex] means
[tex]4=a * b^0[/tex]
[tex]4=a *1[/tex]
[tex]a= 4[/tex]
So, we have:
[tex]y = ab^x[/tex]
[tex]y = 4(3)^x[/tex]
or
[tex]f(x)= 4(3)^x[/tex]
When x is 10, the value of the function is:
[tex]f(x)= 4(3)^x[/tex]
[tex]f(10)= 4(3)^{10[/tex]
[tex]f(10)= 236196[/tex]
