Final answer:
To find the equation of an exponential function that passes through the points (2,48) and (5,750), we need to find the values of the base and the exponent. The equation of the exponential function is y = 7.68(2.5)^x.
Step-by-step explanation:
To find the equation of an exponential function that passes through the points (2,48) and (5,750), we need to find the values of the base and the exponent. Let's assume the function is of the form y = ab^x. We can substitute the values from the given points into the equation to get two equations:
48 = ab^2
750 = ab^5
Now we can divide the second equation by the first equation to eliminate the constant term 'a':
750/48 = (ab^5) / (ab^2)
Simplifying the equation, we get:
15.625 = b^3
Taking the cube root of both sides, we find:
b = 2.5
Now we can substitute this value of 'b' back into one of the original equations to solve for 'a':
48 = a(2.5)^2
Simplifying, we get:
48 = 6.25a
Dividing both sides by 6.25, we find:
a = 7.68
Therefore, the equation of the exponential function is:
y = 7.68(2.5)^x