Modeling Exponential Growth: Equations & Factors

A population of bacteria doubles every 3 hours. If there are initially 500 bacteria, write an exponential equation to represent the population after t hours. What is the growth factor?

• P(t) = 500 * 2^(t/2), growth factor = 2

• P(t) = 500 * 3^(t/3), growth factor = 3

• P(t) = 500 * 2^(t/3), growth factor = 2

• P(t) = 500 * 2^(t/4), growth factor = 4

A car's value decreases by 15% each year. If the car is currently worth $20,000, write an exponential equation to model its value over time. What is the growth factor?

• V(t) = 20000 * (0.85)^t; Growth factor = 0.85

• V(t) = 20000 * (0.75)^t; Growth factor = 0.75

• V(t) = 20000 * (1.15)^t; Growth factor = 1.15

• V(t) = 20000 * (0.90)^t; Growth factor = 0.90

A tree grows at a rate of 10% per year. If the tree is currently 4 feet tall, write an exponential equation to represent its height after t years. What is the growth factor?

• H(t) = 4 * (1.05)^t; Growth factor = 1.05

• H(t) = 4 * (0.90)^t; Growth factor = 0.90

• H(t) = 4 * (1.10)^t; Growth factor = 1.10

• H(t) = 4 * (2.00)^t; Growth factor = 2.00

A savings account earns 5% interest compounded annually. If you start with $1,000, write an exponential equation to represent the amount in the account after t years. What is the growth factor?

• A = 1000(1.03)^t; Growth factor = 1.03

• A = 1000(1.05)^t; Growth factor = 1.05

• A = 1000(1.10)^t; Growth factor = 1.10

• A = 1000(0.05)^t; Growth factor = 0.05

A certain species of fish in a lake increases in population by 25% each year. If the current population is 1,200, write an exponential equation to model the population after t years. What is the growth factor?

• P(t) = 1200 * (1.5)^t; Growth factor = 1.5

• P(t) = 1200 * (0.75)^t; Growth factor = 0.75

• P(t) = 1200 * (1.25)^t; Growth factor = 1.25

• P(t) = 1200 * (2)^t; Growth factor = 2

A smartphone's battery life decreases by 20% each year. If the battery lasts 24 hours when new, write an exponential equation to represent its battery life after t years. What is the growth factor?

• L(t) = 24 * (0.5)^t; Growth factor = 0.5

• L(t) = 24 * (1.2)^t; Growth factor = 1.2

• L(t) = 24 * (0.9)^t; Growth factor = 0.9

• L(t) = 24 * (0.8)^t; Growth factor = 0.8

A viral video on a social media platform gains views at a rate of 30% per day. If it starts with 1,000 views, write an exponential equation to represent the views after t days. What is the growth factor?

• V(t) = 1000 * (0.70)^t; Growth factor = 0.70

• V(t) = 1000 * (1.50)^t; Growth factor = 1.50

• V(t) = 1000 * (1.30)^t; Growth factor = 1.30

• V(t) = 1000 * (1.20)^t; Growth factor = 1.20

A certain type of investment grows by 8% each year. If you invest $5,000, write an exponential equation to represent the value of the investment after t years. What is the growth factor?

• V = 5000(1.08)^t; Growth factor = 1.08

• V = 5000(1.10)^t; Growth factor = 1.10

• V = 5000(2)^t; Growth factor = 2

• V = 5000(1.05)^t; Growth factor = 1.05

A population of rabbits triples every year. If there are currently 150 rabbits, write an exponential equation to represent the population after t years. What is the growth factor?

• P(t) = 150 * 4^t; Growth factor = 4

• P(t) = 150 * 3^t; Growth factor = 3

• P(t) = 150 + 3^t; Growth factor = 3

• P(t) = 150 * 2^t; Growth factor = 2

A new technology is adopted by 15% of the population each year. If 10,000 people are currently using it, write an exponential equation to model the number of users after t years. What is the growth factor?

• N(t) = 10000 * (0.85)^t; Growth factor = 0.85

• N(t) = 10000 * (1.10)^t; Growth factor = 1.10

• N(t) = 10000 * (1.20)^t; Growth factor = 1.20

• N(t) = 10000 * (1.15)^t; Growth factor = 1.15