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Quantitative Method Assignment

Assignment

1. Consider the data for the population of Mexico in the early 1980s in the following table:

Year Population (millions) Change in population (millions)
1980 67.38
1981 69.13
1982 70.93
1983 72.77
1984 74.66
1985 76.60
1986 78.59


To see how the population is growing, you might look at the increase in population from one year to the next. If the population had been growing linearly, all the numbers in the third column (which is kept blank) would be the dame.
(a) Determine whether the data correspond to an exponential function, linear function or neither.
(b) For which could correspond to an exponential or linear function, find a formula /equation for the function.
(c) Predict the population of Mexico in the year (i) 2007 (ii) 2034 and (iii) 2061 and comment.

2. The pitch of a musical note is determined by the frequency of the vibration which causes it. Middle C on the piano, for example, corresponds to a vibration of 263 hertz (cycles per second). A note one octave above middle C vibrates at 526 hertz and a note two octaves above middle C vibrates at 1052 hertz.

Number, n, of octaves above middle C Number of hertz V = f(n)
0 263
1 526
2 1052
3 2104
4 4208

Determine whether the function is linear or exponential and if correspond to an exponential or linear function, find a formula for the function.