Ask Question
12 January, 00:27

Choose all that are best modeled by an exponential function. A town with an initial population of 2,000 doubling in size every 10 years. A car rental that cost $20 a day plus $0.05 per mile. A bank account with a starting balance of $1,000 compounded annually at 5%. A sugar processing plant producing 2 tons of sugar per month.

+4
Answers (1)
  1. 12 January, 04:24
    0
    Exponential functions for the following example will be given as follows:

    a] A town with an initial population of 2,000 doubling in size every 10 years.

    solution:

    The exponential function for this example will be:

    f (t) = ab^ (nt)

    where:

    a=initial size

    b=growth rate

    t=time

    n=number of terms

    thus plugging in our values we obtain:

    f (t) = 2000 (2) ^t/10

    b] A car rental that cost $20 a day plus $0.05 per mile.

    This example will follow a linear equation of the form y=ax+b, where a=rate,

    b=constant amount.

    From our example:

    a=$0.05 per mile

    b=20 dollars per day

    x=number of miles

    Thus the function will be:

    f (x) = 0.05x+20

    c] A bank account with a starting balance of $1,000 compounded annually at 5%.

    Here we shall use the compound interest formula to obtain our value:

    FV=P (1+r/100) ^t

    where:

    FV=future value

    P=principle amount

    r=rate

    t=time

    thus, plugging in our value in the equation we obtain:

    P=$1000; r=5%, time=t

    f (t) = 1000 (1+5/100) ^t

    f (t) = 1000 (1.05) ^t

    Hence the function representing the case is:

    f (t) = 1000 (1.05) ^t

    d] A sugar processing plant producing 2 tons of sugar per month.

    This will be modeled using linear function, such that the total will be given by:

    f (x) = 2x

    where:

    x is the number of months:

    thus the cases that are best modeled by exponential function is:

    A and C
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “Choose all that are best modeled by an exponential function. A town with an initial population of 2,000 doubling in size every 10 years. A ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers