Population Growth Models

Name:

Class:

Date:

Show your work for each problem.

1.
A town of $2000$ people grows by $4\%$ per year. Which function models its population after $t$ years?
1. a) $P(t) = 2000 \cdot 0.04^t$
2. b) $P(t) = 2000 \cdot 1.04^t$
3. c) $P(t) = 2000 + 1.04t$
4. d) $P(t) = 2000 \cdot 4^t$
2.
A population of $6000$ doubles every $15$ years. Which model gives the population after $t$ years?
1. a) $P(t) = 6000 \cdot 2^{15t}$
2. b) $P(t) = 6000 \cdot 2^t$
3. c) $P(t) = 6000 \cdot 2^{t/15}$
4. d) $P(t) = 6000 \cdot 15^{t/2}$
3.
A country's population grows by $2\%$ per year. Using the rule of 70, about how long does it take to double?
1. a)14 years
2. b)35 years
3. c)140 years
4. d)3500 years
4.
A rabbit population on an island grew exponentially for a few years, but now its growth is slowing down. What is the most likely reason?
1. a)The growth factor of an exponential model drops below 1 after a few years
2. b)Populations always switch to linear growth after exactly 5 years
3. c)Food and space are limited, so the population is approaching the carrying capacity
4. d)Exponential functions always reach a maximum value
5.
Town A and town B both have $10000$ inhabitants today. Town A grows by $500$ people per year; town B grows by $5\%$ per year. Which statement about the populations in 20 years is true? (Use $1.05^{20} \approx 2.6533$ .)
1. a)Town B is larger by about 6533
2. b)Both towns have 20000 inhabitants
3. c)Town B is larger by exactly 500
4. d)Town A is larger by about 6533
6.
A colony of $1500$ rabbits grows by $10\%$ per year. How many rabbits are there after 1 year?
7.
A city of $4000$ people doubles every $8$ years. What is its population after $24$ years?
8.
A fish population grows by $7\%$ per year. Use the rule of 70 to estimate its doubling time in years.
9.
A village had $2500$ inhabitants in 2023 and $2600$ in 2024. What is its yearly growth rate in percent? (Write only the number, for example 5.)
10.
A culture of $200$ bacteria doubles every $25$ minutes. After how many minutes will there be $12800$ bacteria?
11.
A town of $30000$ people grows by $2\%$ per year. What is its population after 2 years?
12.
A sample of $50$ bacteria doubles every $10$ minutes. How many bacteria are there after 1 hour?
13.
A lake had $800$ fish last year and has $880$ fish this year. Assuming the same yearly percentage growth, how many fish will there be 2 years after the count of 800?
14.
A country of $5$ million people grows by $1.4\%$ per year. Use the rule of 70 to estimate its population in 100 years (in millions).
15.
A deer population of $1000$ doubles every $10$ years. Estimate the population after $5$ years. (Round $2^{0.5}$ to 3 decimal places.)
16.
A city had $40000$ inhabitants in 2020 and $44000$ in 2021. Forecast 2023 with a linear model and with an exponential model. How much larger is the exponential forecast?
17.
A city had $5000$ inhabitants in 2018 and $7200$ in 2020. Assuming the same yearly percentage growth, predict the population in 2022.
18.
A population of $10000$ grows by $5\%$ per year. Estimate the doubling time with the rule of 70, then check the estimate: how large is the population after that many years?