Question

Consider the exponential functions below.i. f(x) = { (3)*ii. g(x) = 3 )iii. h(x) = 1 ()Which of these functions show exponentialgrowth?a. i onlyb. i and iic. i and iiid. i, ii, and iii

Answer 1

Step 1

An exponential function is a function that has the form of f(x) = abˣ, where b is a positive real number.

Therefore since all the functions are in that form they are all exponential, however, with a graph plot we can determine which of the functions shows an exponential growth or decay.

From the graph above the following functions have exponential growth

f(x) = 1/2(3)ˣ

h(x) = 1(3/2)ˣ

Since their plotted graphs are going up the y-axis

g(x) = 3(1/2)ˣ has an exponential decay.

Another way to ascertain this is functions where the value of b >1

In

f(x) = 1/2(3)ˣ

h(x) = 1(3/2)ˣ

b = 3 and 3/2 respectively and this is more than 1. Therefore they have exponential growth

Therefore, the right answer is option C (I and III)