Regina charges c dollars per hour to babysit. If she increases her rate by 15%, which expression represents her new rate, in dollars per hour?

Answer 1

If Regina asked $20 per hour for babysitting and then did a 15% increase how would you determine her new hourly rate.

Probably something like this.

15% of $20 is 20(.15) equals $3 which is the amount of increase. To get her new hourly rate add $3 to her original to $3+$20 = $23.

Another way to look at it: 20 + 20(.15) = 20(1.15). That is typical when you have a "growth rate". Add the rate of growth (as a decimal) to 1 (the amount started with) to get the multiplicative rate of change, i.e. 1+0.15 = 1.15.

In the given problem instead of $20 we are using the letter "c" to represent her initial hourly rate.

Following the pattern from above.

.15c = the amount of increase.

c+.15c = new hourly rate

1.15c a simplified form for new hourly rate.

Once you get used to the pattern you can go from rate of growth right to the multiplicative rate of change, i.e. 1.15. Then new hourly rate is immediately apparent as 1.15c.

Suppose a population is increasing at a rate of 12% per year. Then rate of change is 1.12.

Rate of decrease works a bit differently. Subtract the rate of decrease from 1 to get multiplicative rate of decay. So if population is decreasing at 5% per year, the decay rate is 1 - .05 = .95. That means that at the conclusion of each year 95% of the original remains.