AP CALCULUS
EXPONENTIAL AND LOGARITHM SUPPLEMENTARY
Problems
:
1)
The Chernobyl nuclear reactor accident in April 1986 released radioactive Cesium–137 into the air.
The half –life of
Cesium–137 is 28 years.
a)
Find a formula
()
Nt
for the amount of Cesium–137 present
t
years after the accident.
b)
In what year will only 25 percent of the originally released radioactive Cesium–137 remain?
c)
How many years will it take for 90 percent of the original Cesium–137 to be transmutated?
2)
A certain type of bacterium increases its numbers every hour by 5% when placed in a suitable growing medium.
Let
the original number of bacteria in the medium be
N
0
.
a)
Find a formula
for the amount of bacteria in the medium
t
hours after the bacteria were placed into the
growing medium.
b)
Calculate how long it will take for the number of bacteria in the medium to triple
.
3)
A roast turkey is taken from an oven when its temperature has reached 170
o
C
and begins to cool exponentially.
a)
If the temperature of the turkey is 140
o
C
after a half hour, then find the temperature after 45 minutes.
b)
When will the turkey have cooled to 40
o
C
?
4)
The population of the Earth was 4 billion on January 1, 1975.
Assuming that the population grows exponentially with
an annual growth rate of 1.5 percent, when will the Earth’s population reach 10 billion?
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 Spring '09
 TANNY
 Calculus, AP Calculus, Logarithm, Hyperbolic function

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