Question

Revisiting Exponential Growth At time t = 0 a population has size 1000. Suppose it grows...

Revisiting Exponential Growth
At time t = 0 a population has size 1000. Suppose it grows exponentially, so that at
time t (years) it has size S(t) = 1000a
t
for some a and all t > 0.
a) Suppose that it doubles in size every 8 years. What is a?
b) After how many years is the population 32 000?
c) What is its instantaneous growth rate (individuals per year) at t = 10?
d) What is its instantaneous per capita growth rate at t = 10?
e) What is its instantaneous percentage growth rate at t = 10?

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Suppose that a population of deer is experiencing exponential growth, with r= 1.5 individuals/year. If the...
Suppose that a population of deer is experiencing exponential growth, with r= 1.5 individuals/year. If the population size now is 4, how many deer will be added to the population in the next year? If necessary, truncate your answer to a whole number. Show your work. Suppose that a population of deer is experiencing exponential growth, with r= 0.89 individuals/year. If the starting population size was 8, how many deer will be in the population after 5 years? If necessary,...
exponential functions Write an equation for each statement. a)The initial population is 279. The population grows...
exponential functions Write an equation for each statement. a)The initial population is 279. The population grows by 37 people per year. Let P be the population and x be the number of years. b) The inital population is 1607. The population doubles every year. Let P be the population and t be the number of years.
1. A population grows according to an exponential growth model. The initial population is P0=12, and...
1. A population grows according to an exponential growth model. The initial population is P0=12, and the common ratio is r=1.45 Then: P1 = P2 = Find an explicit formula for Pn. Your formula should involve n. Pn =    Use your formula to find P9 P9= Give all answers accurate to at least one decimal place 2. Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that...
The per capita growth rate of many species varies temporally for a variety of reasons, including...
The per capita growth rate of many species varies temporally for a variety of reasons, including seasonality and habitat destruction. Suppose n(t) represents the population size at time t, where n is measured in individuals and t is measured in years. Solve the following differential equation. Habitat destruction is modeled as n' = (r − at)n      n(0) = n0. Here the per capita growth rate declines over time, going from positive to negative. It is modeled by the function r −...
1) a) The fox population in a certain region experiences exponential growth with a relative growth...
1) a) The fox population in a certain region experiences exponential growth with a relative growth rate of 8% a year. In 2013, it was estimated that the population was 18, 000. (a) Find a function that models the population t years after 2013. (b) Use the function above to estimate the fox population in the year 2021. (c) After how many years will the fox population reach 25, 000? b) Two observers simultaneously measure the angle of elevation of...
A bacteria culture starts with 1000 bacteria and grows at an exponential rate. After 3 hours...
A bacteria culture starts with 1000 bacteria and grows at an exponential rate. After 3 hours there will be 3000 bacteria. Give your answer accurate to at least 4 decimal places (a) Express the population P after t hours as a function of t. (b) What will be the population after 2 hours? (c) How long will it take for the population to reach 1310?
Suppose we have a whale population that has been declines to 1000 individuals. The growth rate...
Suppose we have a whale population that has been declines to 1000 individuals. The growth rate is 2% a year and the carrying capacity is 10,000. Calculate (use Excel) how many years are needed to have the population recover to 5,000 or more, meaning that during those years, no harvesting can take place. Once the population is recovered, how many whales can be harvested per year in a sustainable way?
The population of a town grows at a rate proportional to the population present at time...
The population of a town grows at a rate proportional to the population present at time t. The initial population of 500 increases by 20% in 10 years. What will be the population in 30 years? (Round your answer to the nearest person.)How fast is the population growing at t = 30? (Round your answer to two decimal places.)
Population Growth Equation In the population growth equation, the letter “r” is defined as the per...
Population Growth Equation In the population growth equation, the letter “r” is defined as the per capita rate of increase, which is the difference between the per capita birth rate (the number of offspring produced per unit of time by an average member of the population) and per capita death rate (average number of deaths in the population per unit time). What does the value of “r” indicate about a population? All of the following characteristics are typical of a...
The size P of a certain insect population at time t​ (in days) obeys the function...
The size P of a certain insect population at time t​ (in days) obeys the function P(t)=600e0.06t. ​(a) Determine the number of insects at t=0 days. ​(b) What is the growth rate of the insect​ population? ​(c) What is the population after 10​ days? ​(d) When will the insect population reach 720? ​(e) When will the insect population​ double?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT