Question

Given the following exponential function, identify whether the change represents

growth or decay, and determine the percentage rate of increase or decrease.
y= 250(1.904)

Answer 1

Explanation:

The exponential function is of the standard form

`y=a(b)^x`

where a is the initial value and b is the growth/decay rate. The rule for growth is if the b value is greater than 1, it's growth; if the b value is less than 1 but greater than 0, it's decay.

The tricky thing about determining the rate of growth is to keep in mind that you are starting with 100% of whatever it is you have and then are adding a certain percent to that. Our initial value is 250. Say, 250 bacteria in a dish. If this b value is 1.904, that means that we are starting with 100% of the 250 bacteria but are adding 90.4% more to it per hour or day or minute. 100% + 90.4% = 190.4%, which in decimal form is 1.904. Our growth rate is 90.4%.

Long story short, if the value of b is greater than 1, move the decimal 2 places to the right to get the percentage. Subtract 100% from that percentage and that difference is your percent increase (aka growth rate).

1.904, moving the decimal 2 places to the right gives you 190.4%

Subtract 100% from 190.4% to get 90.4%. That's the easy way to find the growth rate.