1. ## rate & amount

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? 2. Originally Posted by Patience 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. 3. Originally Posted by Patience 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. 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

4. Originally Posted by Aryth
1. $12,000 -$10,920 = $1080$12000n = \$1080

n = .09

Thus it is a 9% decrease.
so this is a simpler method for number 1, i dont know why i make things so complicated sometimes. do you even know the formula A = Ao*e^rt ?