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14 August, 03:14

Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Match each situation to its corresponding expression. There are 7 trout fish in a pond, and the population doubles every year. Find the population after t years. arrowBoth A company buys a machine for $3,000. The value of the machine depreciates by 7% every year. Find the value of the machine after t years. arrowBoth The initial population of a colony of ants is 300. The number of ants increases at a rate of 1.5% every month. Find the population of ants after t months. arrowBoth A research laboratory is testing a new vaccine on 300 infected cells. The decay rate is 1.5% per minute. Find the number of infected cells after t minutes. arrowBoth

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  1. 14 August, 04:38
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    Step-by-step explanation:

    We will use the pattern f (x) = a (b) ^t where a is the initial value, b is the base of the exponent. All these questions are about exponent function

    A) Number of trout fish in the pound = 7, it means a = 7

    population increases double every year. It means b=2

    f (x) = a (b) ^t

    f (x) = 7 (2) ^t

    B) Cost of machine = $3000

    The value depreciated every year = 7%

    It means 100%-7% = 93% which is equal to 0.93

    Therefore,

    a = 3000

    b = 0.93

    f (x) = a (b) ^t

    f (x) = 3000 (0.93) ^t

    C) Initial population of a colony of ants = 300

    The number of ants increase at a rate of 1.5%

    It means 100%+1.5%=101.5%

    101.5% = 1.015

    Therefore,

    a = 300

    b = 1.015

    f (x) = a (b) ^t

    f (x) = 300 (1.015) ^t

    D) A research laboratory is testing a new vaccine on 300 infected cells

    The decay rate is 1.5% per minute

    It means 100%-1.5% = 98.5%

    98.5% = 0.985

    Therefore,

    a = 300

    b = 0.985

    f (x) = a (b) ^t

    f (x) = 300 (0.985) ^t ...
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