1. The electricity costs of a business decreased from $12,000 one year to $10,920 the next. What is the rate of decrease?
2. If the total bill at a restaurant, including a 15% tip, is $65.32, what was the cost of the meal alone?
1. $12,000 - $10,920 = $1080
$12000n = $1080
n = .09
Thus it is a 9% decrease.
2. Some number a is the original price, so that:
.15(a) + a = $65.32
1.15a = $65.32
a = $56.80
To double check:
$56.80 x .15 = $8.52 <-- That is our tip
$56.80 + $8.52 = $65.32 <-- The price we had before.
So it checks out.
Basically I just used the percent equations:
(Original Value) x n = (New Value)
Which says that some percent n of the original value is the new value.
1. The electricity costs of a business decreased from $12,000 one year to $10,920 the next. What is the rate of decrease?
Using A = Ao*e^rt ............where A is the amount after time t, Ao is the initial amount, r is the rate (in this case, the rate of decrease) and t is the time.
=> 10920 = 12000e^r after 1 year
=> 10920/12000 = e^r
=> 0.91 = e^r
=> r = ln0.91 = -0.094
2. If the total bill at a restaurant, including a 15% tip, is $65.32, what was the cost of the meal alone?
recall that percentage is just a fancy word for "/100" so 15% means 15/100 = 0.15
also recall that in math, "of" means multiply. so 15% of something means 0.15*something. now moving on
Let x be the cost of the meal alone.
So we pay the cost of the meal, plus 15% of the cost of the meal as a tip. so our total cost, which is 65.32 is given by:
65.32 = x + 0.15x = 1.15x
=> 65.32/1.15 = x
=> x = 56.80
so the cost of the meal is $56.80