Frogs – A species of frog’s population grows 24% every year. Suppose 100 frogs are released into a pond. (For some answers, you should round

Question

Frogs – A species of frog’s population grows 24% every year. Suppose 100 frogs are released into a pond. (For some answers, you should round to whole frogs.)

Construct an exponential model for this population.

How many frogs will there be in 5 years?

How many frogs will there be in 10 years?

About when will there be 1000 frogs? (Round to a whole year.)

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Margaret 1 week 2021-10-06T07:20:36+00:00 2 Answers 0

Answers ( )

    0
    2021-10-06T07:21:46+00:00

    Answer:

    293; 869; 11 years

    Step-by-step explanation:

    N: no. of frogs

    t: no. of years

    N = 100(1.24^t)

    N = 100(1.24⁵)

    = 293

    N = 100(1.24¹⁰)

    = 859

    1000 = 100(1.24^t)

    10 = 1.24^t

    lg10 = t×lg1.24

    t = 1/lg1.24

    t = 10.7 = 11 years

    0
    2021-10-06T07:22:07+00:00

    Answer:

    Step-by-step explanation:

    We would apply the formula for exponential growth which is expressed as

    A = P(1 + r)^ t

    Where

    A represents the population after t years.

    t represents the number of years.

    P represents the initial population.

    r represents rate of growth.

    From the information given,

    P = 100

    r = 24% = 24/100 = 0.24,

    The exponential model for this population becomes

    A = 100(1 + 0.24)^t

    A = 100(1.24)^t

    1) When t = 5 years,

    A = 100(1.24)^5

    A = 293

    2) When t = 10 years,

    A = 100(1.24)^10

    A = 859

    3) When A =1000

    1000 = 100(1.24)^t

    1000/100 = (1.24)^t

    10 = (1.24)^t

    Taking log of both sides to base 10, it becomes

    Log 10 = log 1.24^t

    1 = t log 1.24

    1 = 0.093t

    t = 1/0.093

    t = 11 years to the nearest whole year.

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