Answer:
We can use the given points (1, 15) and (3, 375) to create a system of equations and solve for the values of a and b in the exponential function y = ab^x.
When x = 1, y = 15:
15 = ab^1
When x = 3, y = 375:
375 = ab^3
We can solve the first equation for a to get:
a = 15/b
We can substitute this expression for a into the second equation to get:
375 = (15/b)b^3
Simplifying this equation, we get:
375 = 15b^2
Dividing both sides by 15, we get:
25 = b^2
Taking the square root of both sides, we get:
b = ±5
We can use the positive value of b, b = 5, since a negative base would result in a reflection of the exponential curve.
We can substitute this value of b into the first equation to get:
15 = a(5)^1
Simplifying, we get:
15 = 5a
Dividing both sides by 5, we get:
a = 3
Therefore, the exponential function that passes through the points (1, 15) and (3, 375) is:
y = 3(5)^x