Exponential Growth & Decay
A bacterial culture grows by 12% each hour. If it currently contains 50,000 bacteria, how many bacteria will there be after 5 hours?
88,115
50,000(1.12)5
Which function decreases by 10% every time x increases by 1?
f(x)=1.10x
g(x)=0.9x
h(x)=10x
k(x)=90x
g(x)=0.9x
At the beginning of the year, the population of a city was 50,000. Since then, it has grown by 0.5% each month.
Which expressions represent the population, in thousands, 8 years later if it continues to grow at that rate?
a. 50((1+0.005)12)8
b. 50((1+0.005))96
c. 50((1.005)12)8
d. 50(0.995)96
c. 50(0.005)96
b & c
The function C(t)=5.80(0.92)t models the cost in dollars, C(t), of 1 ounce of a certain chemical used in a laboratory. t represents the number of years since 2010.
Does the cost of the chemical increase or decrease over time, and by what percentage per year does it do so?
Decrease by 8%
An investment account earns 7% interest, compounded annually. If you invest $8,000 today, what will the account balance be in 10 years?
$15,738
8,000(1.07)10
Which function decreases by 25% every time x increases by 1?
f(x)=0.75x
g(x)=1.25x
h(x)=25x
k(x)=75x
f(x)=0.75x
At the beginning of the year, a lake contained 2,000 gallons of water. Each month, the amount of water increased by 1.2%.
Which expressions represent the number of gallons, in thousands, after 4 years if the pattern continues?
a. 2((1+0.012)12)4
b. 2((1+0.012))12
c. 2((1+0.012))4
d. 2((1+0.012)4)12
e. 2(1.012)48
a, d, & e
The function C(t)=4.25(1.07)t models the cost in dollars, C(t), of 1 ounce of a certain chemical used in a laboratory. t represents the number of years since 2010.
Does the cost of the chemical increase or decrease over time, and by what percentage per year does it do so?
Increase by 7%
A radioactive isotope decays at a rate of 3% per day. If you start with 20 grams of the isotope, how much will remain after 15 days?
12.74
20(0.97)15
Which function decreases by 5% every time x increases by 1?
f(x)=5x
g(x)=0.5x
h(x)=0.05x
k(x)=0.95x
k(x)=0.95x
At the beginning of the year, a museum had 5,000 art pieces. Every month, the collection grew by 0.75%.
write an expression to represent the number of pieces, in thousands, after 6 years if the trend continues?
5((1+0.0075)12)6
or
5(1+0.0075)72
The function C(t)=9.10(0.85)t models the cost in dollars, C(t), of 1 ounce of a certain chemical used in a laboratory. t represents the number of years since 2010.
Does the cost of the chemical increase or decrease over time, and by what percentage per year does it do so?
Decrease by 15%
A social media influencer’s follower count increases by 20% each month. If they have 120,000 followers now, what will their follower count be after 3 months?
207,360
120,000(1.20)4
Which function decreases by 30% every time x increases by 1?
f(x)=30x
g(x)=0.30x
h(x)=70x
k(x)=0.70x
k(x)=0.70x
At the beginning of the year, a college had 15,000 students enrolled. Each month, enrollment increased by 0.6%.
Write an expression to represent the number of students, in thousands, after 7 years if it continues?
15((1.006)12)7
or
15(1.006)84
The function C(t)=6.75(1.03)t models the cost in dollars, C(t), of 1 ounce of a certain chemical used in a laboratory. t represents the number of years since 2010.
Does the cost of the chemical increase or decrease over time, and by what percentage per year does it do so?
Increase by 3%
A sapling’s height increases by 8% each year. If the tree is currently 1.5 meters tall, how tall will it be in 4 years?
2.04
1.5(1.08)4
Which function decreases by 18% every time x increases by 1?
f(x)=0.82x
g(x)=0.18x
h(x)=18x
k(x)=82x
f(x)=0.82x
At the beginning of the year, a mobile app had 80,000 users. Since then, its user base has grown by 2% each month.
Write an expression to represent the number of users, in thousands, after 2 years if the growth rate continues?
80((1+0.02)12)2
or
80(1+0.02)24
The function C(t)=8.00(0.97)t models the cost in dollars, C(t), of 1 ounce of a certain chemical used in a laboratory. t represents the number of years since 2010.
Does the cost of the chemical increase or decrease over time, and by what percentage per year does it do so?
Decrease by 3%