Answer:
The exponential function is y = [tex]1600(1.25)^{x}[/tex]
Step-by-step explanation:
The form of the exponential function is y = a[tex]b^{x}[/tex], Where
- a is the initial value (value y at x = 0)
- b is the exponential factor
Let us use the form above to solve the question
→ From the given table
∵ At x = 0, y = 1600
∵ from the form above a is the value of y at x = 0
∴ a = 1600
→ Substitute it in the form of the equation above
∴ y = 1600[tex](b)^{x}[/tex]
→ To find b use the point from the table and substitute x and y by its
coordinates
∵ At x = 1, y = 2000
→ Substitute them in the equation
∴ 2000 = 1600[tex](b)^{1}[/tex]
∴ 2000 = 1600(b)
→ Divide both sides by 1600 to find b
∴ 1.25 = b
→ Substitute it in the equation
∴ y = 1600 [tex](1.25)^{x}[/tex]
∴ The exponential function is y = [tex]1600(1.25)^{x}[/tex]
