Question

What is the exponential function of a graph with the points (2,6) and (5,48)

Answer 1

To find the exponential function through the points (2, 6) and (5, 48), we derive the equation y = ab^x, where a and b are constants. By solving a system of equations derived from the given points, we find that the function is y = 1.5*2^x.

Step-by-step explanation:

To find the exponential function that passes through the points (2, 6) and (5, 48), you need to write the equation in the form y = abx, where a is the initial value and b is the base or growth factor.

Let's start with the point (2, 6). We have 6 = a*b2. Next, using the point (5, 48), we get 48 = a*b5. We can create a system of equations using these two equations:

1. 6 = a*b2
2. 48 = a*b5

Divide the second equation by the first one to find b:

b3 = 48/6
b3 = 8
b = 2

Now plug the value of b back into the first equation to solve for a:

6 = a*22

6 = a*4
a = 1.5

Thus, the exponential function is y = 1.5*2x.