Exponential Growth And Decay Equation Worksheet With Answer Key Page 2
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4SOLVING EXPONENTIAL GROWTH AND DECAY PROBLEMS
Example 1
Example 2
Movie tickets now average $9.75 a ticket, but
A powerful computer is purchased for $2000,
are increasing 15% per year. How much will
but on the average loses 20% of its value each
they cost 5 years from now?
year. How much will it be worth 4 years from
now?
The equation to use is: y = ab
x
. The initial
The equation to use is: y = ab
x
. The initial
value a = 9.75 . The multiplier b is always
value a = 2000 . In this case the value is
found by adding the percent increase (as a
decimal) to the number "one," so
decreasing so multiplier b is always found by
b = 1 + 0.15 = 1.15 . The time is x = 5 .
subtracting the percent decrease from the
number "one," so b = 1 ! 0.2 = 0.8 . The time
Substituting into the equation and using a
is x = 4 . Substituting into the equation and
calculator for the calculations:
using a calculator for the calculations:
y = ab
= 9.75(1.15)
! 19.61 . In five years
x
5
y = ab
= 2000(0.8)
= 819.2 . In four years
x
4
movie tickets will average about $19.61.
the computer will only be worth $819.20.
Example 3
Example 4
Dinner at your grandfather's favorite restaurant
If a gallon of milk costs $3 now and the price
now costs $25.25 and has been increasing
is increasing 10% per year, how long before
steadily at 4% per year. How much did it cost
milk costs $10 a gallon?
35 years ago when he was courting your
In this case we know the starting value a = 3 ,
grandmother?
the multiplier b = 1.1 , the final value y = 10 ,
The equation is the same as above and
but not the time x. Substituting into the
a = 25.25 , b = 1.04 , but since we want to go
= 10 . To solve this,
equation we get 3(1.1)
x
back in time, x = !35 . A common mistake is
you will probably need to guess and check
to think that b = 0.96 . The equation is
with your calculator. Doing so yields
!35
y = ab
= 25.25(1.04)
" 6.40 .
x
x ! 12.6 years. In Algebra 2 you will learn to
solve these equations without guess and check.
Problems
5.
The number of bacteria present in a colony is 180 at 12 noon and the bacteria grows at
a rate of 22% per hour. How many will be present at 8 p.m.?
6.
A house purchased for $226,000 has lost 4% of its value each year for the past five
years. What is it worth now?
7.
A 1970 comic book has appreciated 10% per year and originally sold for $0.35. What
will it be worth in 2010?
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