Answer: y = 14 * 5^x
Explanation:
To find the equation of an exponential function in the form y = ab^x that passes through the points (0, 14) and (4, 8750), we can use the following steps:
Step 1: Use the point (0, 14) to find the value of a.
When x = 0, the equation becomes y = ab^0 = a(1) = a. Therefore, we know that the y-intercept of the function is a = 14.
Step 2: Use the point (4, 8750) to find the value of b.
Substitute x = 4 and y = 8750 into the equation y = ab^x:
8750 = 14b^4
Solve for b:
b^4 = 8750/14
b^4 = 625
b = 5 (since b is positive)
Step 3: Write the equation using the values of a and b.
The exponential function that passes through the points (0, 14) and (4, 8750) is:
y = ab^x
y = 14(5)^x
Therefore, the equation is y = 14 * 5^x.