answers to Additional Growth-related Problems

( 1) 70 is __0.01__ times 7000.
( 2) __18__ is 3 times 6.
( 3) 6 times __0.5__ is 3.
( 4) __2__ times 3 is 6.

( 5) __51__ is 1.7% of 3000.
( 6) __0.1%__ of 800 is 0.8
( 7) 400% of __9__ is 36.
( 8) 7.50 is __250%__ of 3.
( 9) 1.08 is 9% of __12__.
(10) __30%__ of 0.7 is 0.21
(11) 80% of __80__ is 64.
(12) 160% of 300 is __480__.
(13) 75 is __18.75%__ of 400.
(14) __7__ is 0.25% of 2800.
(15) 85 is __170%__ of 50.
(16) 0.7% of 4 is 0.028

(17) The keyword for this unit is __multiplier__.
(18) The price of coffee beans went from $7.50 to $9.00 per pound.
     The price of coffee beans increased __20__%.
     The new price of coffee beans is __1.20__ times the old price.
(19) The weight of a Featherlite bicycle went from 20 pounds to 17 pounds.
     The weight of the bicycle is __15__% lower than before.
     The new weight of the bicycle is __85__% of the old weight.
(20) The price of a guitar went from $700 to $280.
     The new price of the guitar is __0.4__ times the original price.
     You pay __40__% of the original price.
     You save __60__% of the original price.
(21) If an amount goes up 3%, the new amount will be __1.03__ times the old amount.
(22) If an amount goes up 30%, the new amount will be __1.30__ times the old amount.
(23) If an amount goes up 300%, the new amount will be __4.00__ times the old amount.
(24) If an amount drops 3%, the new amount will be __0.97__ times the old amount.
(25) If an amount drops 30%, the new amount will be __0.70__ times the old amount.
(26) Multiplying a number by 0.2 is the same as decreasing the number __80__%.
(27) Multiplying a number by 1.2 is the same as increasing the number __20__%.
(28) Multiplying a number by 2.0 is the same as increasing the number __100__%.
(29) Multiplying a number by 0.6875 is the same as __decreasing__ the number __31.25__%.
(30) Multiplying a number by 27.5 is the same as __increasing__ the number __2650__%.
(31) If you want to raise a price 9% in one step, just multiply it by __1.09__.
(32) If you want to lower a price 90% in one step, just multiply it by __0.10__.

(33) If the price of a shirt (not including sales tax) is $17, how much will the shirt cost with 1.8% sales tax?
	$17.31
(34) Suppose the sales tax rate is 2.9%.
     If you paid $874.60 (including sales tax) for a pool table, what was the price of the pool table (before tax)?
	$849.95
(35) Applying a 32% mark-up followed by a 45% mark-up has the same effect as a __91.4__% mark-up.
(36) The net result of following a 50% discount by another 50% discount is a __75__% discount.
(37) The net result of following a 50% increase by another 50% increase is a __125__% increase.
(38) The net result of following an 80% mark-up by a 36% discount is a __15.2__% __mark-up__.
(39) A 25% mark-up followed by a 25% discount does <I>not</I> bring a price back to its original value.
     What percent discount <I>would</I> "cancel out" a 25% mark-up?
	a 20% discount
(40) What percent discount would "cancel out" a 70% mark-up?
	a 41.2% discount

(41) Suppose that Photonics, Inc. stock has gone through the following price changes over the past years:
     +3%, -14%, +15%, +92%, +65%, +35%, -89%, +79%, +32%, +38%, +46%
     What is the net change in price?
	UP 128.1% (a 128.1% increase)
(42) Suppose the population of Urgency has been going down 2% every year.
     If the population of Urgency 42 years ago was 5000, what is the population today?
	2140
(43) Suppose the population of Vitality has been going up 2.7% every year.
     If the population of Vitality 43 years ago was 5000, what is the population today?
	15,722
(44) Suppose you put $2000 into a savings account that earns 3.5% annual interest.
     How much will be in the account after 11 years?
	$2919.94
(45) Suppose you put $5000 into an account that grows 9% annually, compounded monthly.
     What will be the future value in 12 years?
	$14,664.18
(46) Suppose you put $21,000 into an account at 7% annual interest, compounded quarterly.
     What will be the FV in 17 years?
	$68,321.86
(47) Suppose you have an account that earns 8.33% annual interest.
     How much would you have to put into the account now so that you will have $47,000 in 18 years?
	$11,133.21
(48) Suppose you have an account that earns 7.2% annual interest, compounded quarterly.
     How much would you have to put into the account now so that you will have $32,000 in 19 years?
	$8247.43
(49) Suppose you have an account that earns 4.7% annual interest, compounded monthly.
     How much would you have to put into the account now so that you will have $7000 in 20 years?
	$2739.42
(50) Suppose carbon-14 decays so that it loses 0.012% of its weight every year.
     If 3 oz. of carbon-14 in a fossil started to decay 5000 years ago, how much should it weigh today?
	3(0.99988^5000) = 1.646 oz.
(51*) If the carbon-14 in an object should have weighed 21 grams when it started to decay,
     and weighs 17 grams today, about how old is the object?
	about 1700-1800 years