Laws of Exponents
Simplify x2*x9
x11
A savings account starts with $500 and earns 4% interest compounded annually. The balance after t years is modeled by: A(t) = 500(1.04)ᵗ
What is the initial value?
500
A coffee shop opens with 3 locations. The number of locations doubles every year. Write a function for the number of locations after t years.
f(t)= 3(2)t
A town has 12,000 residents and grows 2% annually:
What is the population after 8 years?
14060 people
3 + 6 × (5 + 4) ÷ 3 − 7
14
Simplify (12x3y4)2
144x6y8
A population of 8,000 bacteria triples every hour. After t hours: P(t) = 8000(3)ᵗ
What is the growth factor?
3
A flu outbreak begins with 5 infected students. The number of cases quadruples each day. Write a function for infected students after d days.
f(t)= 5(4)t
An investment of $2,000 earns 6% interest compounded annually:
What is the worth after 5 years?
$2676.45
2³ + (12 − 4) × 2 − 5
19
Simplify (10x-2)(2x6)
20x4
A car purchased for $24,000 depreciates at 15% per year. Its value after t years: V(t) = 24000(0.85)ᵗ
What is the decay factor?
0.85
A gym membership starts at $75/month and increases by 8% per year. Write a function for the monthly cost after t years.
f(t) = 75(1.08)t
A scientist starts with 100 mg of medicine that decays 25% per hour:
What medicine remains after 6 hours?
17.80mg
5 × (3 + 2)² − 4 × 3 + 1
114
Simplify (x8y2)/(xy4)
x7/y2
A social media post has 50 views and the views increase by 120% each day. Model: V(t) = 50(2.2)ᵗ
What is the percent increase in decimal form?
1.2
A $1,200 laptop loses 20% of its value each year. Write a function for its value after t years.
f(t)=1200(0.80)t
A phone is bought for $800 and depreciates 18% per year:
What is the value after 3 years
$441.09
18 ÷ (9 − 6) + 4² − 2 × 3
16
Simplify (9xy2)0*x4
x4
A radioactive sample starts with 200 grams and loses 30% of its mass each year. Model: M(t) = 200(0.70)ᵗ
What is the decay percentage as a decimal?
0.3
A city has a population of 45,000 and grows at a rate of 3.5% per year. Write a function for the population after t years.
f(t)=45000(1.035)t
A wildfire begins burning 2 acres and the area triples every day:
How many acres are on fire after 5 days?
486 acres
(7 + 3) × 2² ÷ (6 − 1) + 8
16