Answer:
[tex]\boxed{ f(x) = 135(2.256)^{x}}[/tex]
Step-by-step explanation:
An exponential function has the general form
[tex]f(x) = ab^{x}[/tex]
Your function passes through the points (0, 135) and (5, 7890).
If we substitute the values of the points, we get two equations:
[tex]\begin{array}{rrcll}(1)&135& = & a(b)^{0} & \\(2)&7890 & = & a(b)^{5} & \\(3)& a & = & 135 & \text{Simplified (1)}\\ &7890 & = & 135(b)^{5} & \text{Substituted (3) into (2)}\\ & b^{5} & = & 58.44 & \text{Divided each side by 135}\\ & b & = & 2.256 &\text{Took the fifth root of each side}\\\end{array}\\[/tex]
Thus, the explicit equation is
[tex]\boxed{ f(x) = 135(2.256)^{x}}[/tex]
The figure below shows the graph of your function passing through (0, 135) and (5, 7890).
