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    Exponential and Logarithmic functions

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    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Sales and Advertising: The sales S (in thousands of units) of a product after x hundred dollars is spent on advertising is: S = 10(1-e^kx). When $500 is spent on advertising, 2500 units are sold.

    (a) Complete the model by solving for K.
    (b) Estimate the number of units that will be sold if advertising expenditures are raised to $700.

    © BrainMass Inc. brainmass.com December 24, 2021, 4:51 pm ad1c9bdddf
    https://brainmass.com/math/basic-algebra/exponential-logarithmic-functions-example-problems-11917

    SOLUTION This solution is FREE courtesy of BrainMass!

    Sales and Advertising: The sales S (in thousands of units) of a product after x hundred dollars is spent on advertising is S=10(1-e^kx). When $500 is spent on advertising, 2500 units are sold.

    (a) Complete the model by solving for K.
    (b) Estimate the number of units that will be sold if advertising expenditures are raised to $700.

    (a) Complete the model by solving for K.
    S=10(1-e^kx).

    Sales= S= 2500 =2.5 in thousands
    Advertising= x= 500 =5 (in hundreds)

    Therefore 2.5=10 * (1-e^5k)

    or (1-e^5k)=2.5/10=0.25
    or (1-0.25)=e^5k
    or ln 0.75=5k
    or k=ln 0.75/5= -0.057536

    (b) Estimate the number of units that will be sold if advertising expenditures are raised to $700.

    S=10(1-e^kx)=10(1-e^(-0.057536x))

    x= 700 =7 in hundreds

    S=10(1-e^(-0.057536*7))= 3.315221387 (in thousands)

    = 3315 units

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 4:51 pm ad1c9bdddf>
    https://brainmass.com/math/basic-algebra/exponential-logarithmic-functions-example-problems-11917

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