# Algebra

The fox population in a certain region has a relative growth rate of 5% per year. It is estimated that the population in 2013 was 18,000.
(a) Find a function
n(t) = n0ert
that models the population t years after 2013.
n(t) =

(b) Use the function from part (a) to estimate the fox population in the year 2021. (Round your answer to the nearest whole number.)
26853

foxes

(c) After how many years will the fox population reach 27,000? (Round your answer to one decimal place.)
8

yr

(d) Sketch a graph of the fox population function for the years 2013–2021.

1. 👍 0
2. 👎 0
3. 👁 77
1. a 5% growth per year, starting at 18000 means n(t) = 18000 * 1.05^t
Since 1.05 = e^(ln 1.05) that makes
n = 18000 (e^(ln 1.05))^t
n = 18000 e^(ln 1.05 * t)
n = 18000 e^(.0488t)
Now you can answer the other questions.

1. 👍 0
2. 👎 0
👨‍🏫
oobleck
2. looks like you missed d)
18000 e^(0.05t) = 27000
e^(.05t) = 1.5
take ln of both sides and use log rules
.05t = ln1.5
t = ln1.5/.05 = appr 8.1 years past 2013

1. 👍 0
2. 👎 0
👨‍🏫
Reiny

## Similar Questions

1. ### Math

he world population at the beginning of 1990 was 5.3 billion. Assume that the population continues to grow at the rate of approximately 2%/year and find the function Q(t) that expresses the world population (in billions) as a

2. ### Algebra

I know I can use the population growth formula. here is the question; The fox population in a certain region has a relative growth rate of 7% per year. It is estimated that the population in 2005 was 19,000. (a) Find a function

3. ### Math

A population doubles every 18 years. Assuming exponential growth find the following: (a) The annual growth rate: (b) The continuous growth rate is

4. ### College Algebra

The fox population in a certain region has an annual growth rate of 9% per year. In the year 2012, there were 20,700 foxes counted in the area. What is the fox population predicted to be in the year 2020? Round to the nearest fox.

1. ### math

The population of the world was 7.1 billion in 2013, and the observed relative growth rate was 1.1% per year. (a) Estimate how long it takes the population to double. (Round your answer to two decimal places.) _______yr (b)

2. ### Algebra

The exponential function f(x) = 3(5)x grows by a factor of 25 between x = 1 and x = 3. What factor does it grow by between x = 5 and x = 7? A) 5 B) 25 C) 125 D) 625 3) If a city that currently has a population of 1000 triples in

3. ### Calculous Pre

A population grows from 11,000 to 15,000 in three years. Enter your answers to three decimal places. Assuming the growth is exponential, find the growth rate and continuous growth rate Growth rate ______ %? Continuous rate

4. ### precalculus

A population doubles every 30 years. Assuming exponential growth find the following: annual growth rate: % continuous growth rate: %

1. ### Math

Assume the carrying capacity of the earth is 9 billion. Use the 1960s peak annual growth rate of 2.1​% and population of 3 billion to predict the base growth rate and current growth rate with a logistic model. Assume a current

2. ### SS HELP PLZ ASAP

1) The science that studies population distribution and change is called _________(1 point) A. demography B. geography C. economy D. sociology 2) Canada is bigger than the united states, but only has _______ as many people.(1

3. ### maths

Mr. and Mrs. Fox have each contributed \$1825.00 per year for the last eight years into RRSP accounts earning 6.93% compounded annually. Suppose they leave their accumulated contributions for another five years in the RRSP at the

4. ### Algebra

The fox population in a certain region has an annual growth rate of 10℅ per year. In the year 2012, there were 2100 foxes counted in the area. What is the fox population predicted to be in the year 2018? Round to the nearest