Math

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The population of a city has been decreasing exponentially since 1990. In 1990, the population was 1,000,000. In 2010, the population was 560,000. If t represents time in years since 1990, which of the following equations best models the decay of the population?

1.

y = 1,000,000(0.98)t
2.

y = 560,000(0.98)t
3.

y = 1,000,000(1.02)t
4.

y = 560,000(1.02)t

  • Math -

    think !
    1. It starts in 1990 at 1,000,000
    2. it DECREASES

    and you meant to the POWER t, not times t
    a k^t not a k t
    to check
    at 2010, t = 20 years
    y = 1,000,000* .98^20 ?

  • Math -

    First of all looking at your choices, only 1. and 2. are logical, the other two would show an increase not a decrease, so ....

    let the rate be r
    560000 = 1000000 r^10
    .56 = r^10
    take 10th root of both sides using your calculator
    .56^(1/10) = r
    r = .94367..

    so y = 560000(.94)^t would be it using 2 decimals like all their answers
    I don't see that choice!!!

    check:
    .94367^10 = .560017...
    .560017...(1000000) = 560,017 close enough
    My answer is correct

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