Question

Write an exponential function for the graph that passes through the points (–1, 0.8) and (2,100)

Answer 1

y = 4(5)^x

Explanation:

We can use the form y = ab^x to write the exponential function that passes through the given points.

First, we need to find the values of a and b. We can use the two points to create a system of equations:

0.8 = ab^(-1)

100 = ab^(2)

We can solve for a by multiplying the first equation by b and substituting it into the second equation:

100 = ab^(2)

100 = (0.8b)b^2

125 = b^3

b = 5

Now we can solve for a using either of the original equations:

0.8 = ab^(-1)

0.8 = a/5

a = 4

Therefore, the exponential function that passes through the given points is:

y = 4(5)^x