Transcript growth and decay

Miss P- Algebra
Name___________________________________
Growth and Decay MDT
Date________________ Algebra____
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1) Write out the Exponential Growth / Decay formula:
____________________________________________________
What does each variable stand for: A=____________, r = ______________, t =
_____________________
2) The population of a school of fish increases at a rate of 18% a month. There are currently 500 fish in the school.
a. how many fish will there be in 3 months?
b. how many fish will there be in 2 years?
3) A rock of radioactive material decays at a rate of 8% an hour, there are currently 145 atoms in the rock.
a. how many atoms will there be in 5 hours?
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b. how many atoms will there be in 1 day?
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4) Simon’s credit card bill is $300. The interest rate on the bill is 7.5% a month, if he doesn’t pay the bill at all, how muc
will he owe one year?
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5) Consider the following equation: y = 250 ⋅ 0.75 and answer the following:
a. does this represent exponential growth or decay?
b. What is the original amount in this equation?
c. What is the rate as a percent?
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6) The amount of money in Carmen’s saving account is represented by Y= 3500 (1.04)t where t is the number of months
the money has been in the account.
a. does this represent growth or decay?
b. what is the interest rate on the account (as a percent)?
c. what was the initial amount of money in the bank?
d. how much money will Carmen have in 1 year?
e. After how many months will Carmen have around (use guess and check to figure this one out!)
7) The amount of money M accrued at the end of
n years when a ceratin amount P invested at a
compount annual rate r is given by
M = P(1 + r) t. If a person invests $150 at 5%
interest compounded annually, find the
approximate amount obtained after 5 years
A) 191
C) 1139
8) A population of 5000 doubles in sive every 10
years. Which equation relates the size of the
population y to the number of 10 year periods
in x?
A) y = 2 ⋅ 5000 x
B) y = 5000 ⋅ 2 x
C) y = 10 ⋅ 2
D) y = 5000 ⋅ 10
x
x
B) 4500
D) 900
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9) Which equation represents exponential decay?
A) y = 3 ⋅ (−2) x
C) y = 3.4 ⋅ 0.33
B) y =
x
1 x
⋅2
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D) y = 0.5 ⋅ 1.2
x
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10) Write and solve an exponential function to
model the situation and find the value after the
given time, Round to the nearest whole number.
$20,000 purchase, 6% loss in value each
year, 17 years.
A) y = 20000 ⋅ 1.06 ,
x
B) y = 20000 ⋅ 0.94
x
$50,907
,
$7,431
C) y = 20000 ⋅ 0.94 ,
$6,986
D) y = 20000 ⋅ 1.06 ,
$53,855
x
x
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