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Anonymous asked in Science & MathematicsMathematics · 2 months ago

9th grade algebra?

 Predict how long it will take for the population to reach 500.

thank you!

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3 Answers

  • 1 month ago

    Not quite sure whether 'logarithms' are familiar to you in the 9th grade.

    We can say, P(t) = 225 x (1.15)ᵗ

    The 1.15 part is the annual increase of 15% and t is the time in years. 

    so, after year 1 we would have 225 x 1.15

    after year 2 we would have 225 x 1.15 x 1.15...e.t.c.

    After 5 years we have, 225 x 1.15⁵ = 3 s.f.

    After 6 years we have, 225 x 1.15⁶ = 3 s.f.

    so, the population reaches 500 between 5 and 6 years.

    If you are ok with logarithms we can say:

    500 = 225 x (1.15)ᵗ

    so, 1.15ᵗ = 500/225

    or, ln(1.15ᵗ) = ln(20/9)

    i.e. tln(1.15) = ln(20/9)

    Hence, t = ln(20/9)/ln(1.15) => 5.7 years


  • Bryce
    Lv 7
    2 months ago

    500= 225*1.15^t

    20/9= 1.15^t

    ln(20/9)= tln1.15

    t≈ 5.71 years

  • Anonymous
    2 months ago

    That would be a 5th grade question when I went to school. 

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