Question

Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y = 68(1.04)^x

Answer 1

Answer:

Step-by-step 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 68.  Say, 68 bacteria in a dish.  If this b value is 1.04, that means that we are starting with 100% of the 68 bacteria but are adding 4% more to it per hour or day or minute.  100% + 4% = 104%, which in decimal form is 1.04.  Our growth rate is 4%.

So, long story short, if the b value is greater than 1, move the decimal 2 places to the right and subtract 100 from that number and that's your growth rate.

Our b is 1.04.  Move the decimal 2 places to the right to get 104.  Subtract 100 from 104 to get 4, and that's the percent increase (aka the growth rate).