Pre - CALCULUS

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For the data set shown by the table,
a. Create a scatter plot for the data. (You do not need to submit the scatter plot)

b. Use the scatter plot to determine whether an exponential function or a logarithmic function is
the best choice for modeling the data.

Number of Homes Built in a Town by Year

years

1985
1991
1994
1997
2002

number of home

12
91
145
192
224

  • Pre - CALCULUS -

    well, I can not graph it very well but if exponential then
    y = Ae^kx
    x = year - 1985
    12 = A e^0 = A(1) = A
    so y = 12 e^kx
    in 1994, x = 9 years
    y = 12 e^9k = 145
    e^9k = 145/12 = 12
    9 k = ln 12 = 2.48
    k = .276
    now in 2002 we would get
    x = 17
    then we would get
    y = 12 e^(17*.276)
    y = 12 e^4.69
    y = 1311 whoops, the data shows 224
    not much of a fit
    now try
    ln fit and see if it is better

  • Pre - CALCULUS -

    You can do the rest here , Thank you by the way !

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