FROM THE GIVEN INPUT AND OUTPUT FIND THE EXPONENTIAL FUNCTION

Find an exponential function having the given values.

Problem 1 :

f(0) = 3 and f(1) = 15

Solution :

Exponential function will be in the form

y = ab^x

From the given inputs and outputs, we can understand that the points (0, 3) and (1, 15) on the exponential function.

Applying the values of a and b, we get the required exponential function

y = 3(5)^x

Problem 2 :

f(0) = 5 and f(3) = 40

Solution :

Exponential function will be in the form

y = ab^x

From the given inputs and outputs, we can understand that the points (0, 5) and (3, 40) on the exponential function.

Applying the values of a and b, we get the required exponential function

y = 5(2)^x

Problem 3 :

f(0) = 64 and f(2) = 4

Solution :

Exponential function will be in the form

y = ab^x

From the given inputs and outputs, we can understand that the points (0, 64) and (2, 4) on the exponential function.

Applying the values of a and b, we get the required exponential function

y = 64(1/4)^x

Problem 4 :

f(0) = 80 and f(4) = 5

Solution :

Exponential function will be in the form

y = ab^x

From the given inputs and outputs, we can understand that the points (0, 80) and (4, 5) on the exponential function.

Applying the values of a and b, we get the required exponential function

y = 80(1/2)^x

Problem 5 :

f(2) = 10 and f(4) = 40

Solution :

Exponential function will be in the form

y = ab^x

From the given inputs and outputs, we can understand that the points (2, 10) and (4, 40) on the exponential function.

Applying the value of b², we get

10 = 4a

a = 10/4

a = 5/2

Applying the values of a and b, we get

y = (5/2)(2)^x