Exponential Growth Problem

Question

Identify the following functions as either growth, decay, or neither

f(x) = 2(1.03)^x

g(x) = 5(0.25)^10

h(x) = 0.25(5.06)^x

j(x) = 0.06(-4.02)^x

Answer 1

What determines whether something is exponential growth or decay is whether the growth factor is greater than or less than 1.

If you multiply by a number greater than 1 your product will always increase. On the other hand if you multiply by less than 1 you will always get a smaller amount.

so

1) growth factor is 1.03 which is >1 so this is exponential growth

2 growth factor is .25 which is <1 so this is exponential decay

3) growth factor is 5.06 which is >1 so this is exponential growth

the last one is neither since if you raise a negative number to an odd power you get a negative number and if you raise it to an even power you get a positive number