Answer:
The exponential function will be [tex]f(x) = 5(2)^{x}[/tex]
Step-by-step explanation:
Let the exponential function is given by [tex]f(x) = a(b)^{x}[/tex] ............ (1)
Now, ordered pairs (2,20) and (3,40) are the solution of the above exponential function. So, they will satisfy the equation.
Now, for the ordered pair (2,20) putting f(2) = 20, we get
[tex]20 = a(b)^{2}[/tex] ............. (2)
Again, for the ordered pair (3,40) putting f(3) = 40, we get
[tex]40 = a(b)^{3}[/tex] ............. (3)
Now, from equations (3) and equation (2) we get,
2 = b
⇒ b = 2.
Now, from equation (2) we get, [tex]20 = a(2)^{2} = 4a[/tex]
⇒ a = 5
Therefore, the exponential function will be
[tex]f(x) = 5(2)^{x}[/tex] (Answer)
