Question

Which of the following options results in a graph that shows exponential decay?

f(x) = 0.6(2)x
f(x) = 3(0.7)x
f(x) = 0.4(1.6)x
f(x) = 20(3)x

Answer 1

If the base to which the power is taken is < 1 then its exponential decay.

B becuase of the 0.7

Answer 2

We need to find the function that represents the exponential decay.

We are given options:

f(x) = 0.6(2)^x

f(x) = 3(0.7)^x

f(x) = 0.4(1.6)^x

f(x) = 20(3)^x.

Standard form of an exponential function is
`f(x)=a(b)^x`.

Where a is the initial value and b is the growth or decay factor.

If value of b is less than 1 then it would be an exponential decay.

In the second option we are given f(x) = 3(0.7)^x, the value of b is 0.7.

That is less than 1.

Therefore, f(x) = 3(0.7)^x function shows exponential decay.