Which of the following exponential functions goes through the points (1, 20) and (2, 80)?
f(x) = 5(4)^-x
f(x) = 4(5)^-x
f(x) = 5(4)^x
f(x) = 4(5)^x

Solution:

We know that an exponential function is written as

y = ab^x … (1)

Where a is the initial value

b is the non negative number

The given points are (1, 20) and (2, 80)

Substituting these points in equation (1)

For (1, 20)

20 = ab ….. (2)

For (2, 80) 

80 = ab² …. (3)

Dividing equation (3) by (2)

b = 4

By substituting the value of b in equation (2)

20 = a(4)

a = 5

So we get

y = 5.4^x

Therefore, the exponential function y = 5.4^x goes through the points (1, 20) and (2, 80).

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Which of the following exponential functions goes through the points (1, 20) and (2, 80)?

Summary:

The exponential function y = 5.4^x goes through the points (1, 20) and (2, 80).