Use the information given in the graph to find the exponential function that represents the graph, then find f(5) . Round the answer to two decimal places. (2 points) f(x)= ⋅ x f(5)= (0,8), (1,4), (2,2)

Answer 1

To find the exponential function that represents the given graph, we can use the point-slope form of an exponential function.

The equation in point-slope form is given by: y - y1 = m(x - x1)

Using the points (0,8) and (1,4), we can find the slope (m):
m = (4 - 8) / (1 - 0) = -4

Substituting the slope and the point (0,8) into the point-slope form, we get:
y - 8 = -4(x - 0)
y - 8 = -4x
y = -4x + 8

Therefore, the exponential function that represents the graph is f(x) = -4x + 8.

To find f(5), we substitute x = 5 into the function:
f(5) = -4(5) + 8
f(5) = -20 + 8
f(5) = -12

Rounding to two decimal places, f(5) is approximately -12.