Algebra II Help

4) The function f(x)=2(3)^x represents the growth of a dragonfly population every year in a remote swamp. Rose wants to manipulate the formula to an equivalent form that calculates seven times a year, not just once a year. Which function is correct for Rose’s purpose and what is the new growth rate?
A) f(x)=2(3)^x, growth rate 200%
B) f(x)=2(1.17)^7x, growth rate 17%
C) f(x)=2(3)^x,growth rate 2%
D) f(x)=2(1.17)^x,growth rate 2%

I do not know what to do with this question. I am very confused. I'm thinking it is B or D, but maybe D?
Please explain this to me!! :)

  1. 👍
  2. 👎
  3. 👁
  1. If I understand your question correctly, this is the same as finding the equivalent of an annual rate with new compounding frequencies
    the way it stands, f(x) = 2(3)^x
    or f(x) = 2( 1 + 2)^x to me represents a growth of 200% compounded annually
    so you want
    f(x) = 2(1 + r)^7x to be equivalent

    2(3)^x = 2(1+r)^7x
    3^x = (1+r)^7x
    take log of both sides
    x log3 = 7x log (1+r)
    log 3 = 7log(1+r)
    log3 = log( (1+r)^7)
    3 = (1+r)^7
    take 7th root of both sides
    1.16993 = 1+r
    r = .16993 or 16.993%

    so f(x) = 2(1.16993)^(7x) should do it
    which looks like B

    1. 👍
    2. 👎
  2. I was going to check this:
    e.g how much after 3 years
    f(3) = 2(3)3 = 54
    new one:
    f(3) = 2(1.16993)^21 = 53.9992 , not bad
    According to B
    f(3) = 2(1.17)^21 = 54.067 ,

    so it is B

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Exponential Growth and Decay

    Can somebody please check my answers? 1. Identify the initial amount a and the growth factor b in the exponential function. g(x)=14*2^x a)a=14, b=x b)a=14, b=2

  2. Math

    1. Which function represents an initial population that increases 22% per year where A represents the initial value and X represents time in years? A. Y=A(0.22)^x B. Y=A(0.68)^x C. Y=A(1.22)^x D. Y=A(1.68)^x I do not get how to

  3. 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

  4. 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

  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. 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

  3. precalculas

    the population of preston is 89000 and is decreasing by 1.8% each year A:Write a function that models the population as a function of time t b predict when the population will be 50000

  4. Social Studies

    Natural increase can be best defined as a. population growth that occurs due to people's desire to migrate to more desirable locations. b. population growth that occurs due to an increase in the birthrate.*** c. population growth

  1. Calculus

    A tree grows 2.80 m during the first year since it was planted. During each subsequent year the tree's growth is 85% of its growth the previous year. a) Calculate to the nearest 0.001m, the growth of the tree in the fourth year.

  2. math

    the population growth of a city is modeled by P(t)=240,360e^.012t where t represents the number of years since 2000 a) what is the yearly growth rate as a percent? b) find the population in 2015 c) how long, to the nearest year,

  3. Math - Derivative of a polynomial function(check)

    The red squirrel population, p, in a neighborhood park can be modelled by the function p(t)= srqt(210t+44t^2), where t is time in year. a) Determine the rate of growth of the squirrel population at t= 2years Ans: find the 1st

  4. Calculus

    The rate of growth of a particular population is given by dP/dt=50t^2-100t^3/2 where P is the population size and t is the time in years. The initial population is 25,000. Find the population function. Estimate how many years it

You can view more similar questions or ask a new question.