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Consider the formula P = 67.38 · (1.026)t. If we let P represent the population
of Mexico in year t where t is the number of years from 1980, confirm that
this formula gives the same population values as those given in the table in
Example 6.5.

Year: Population in Millions:
1980              67.38
1981               69.13
1982              70.93
1983              72.77
1984              74.66
1985              76.60
1986              78.59

Explain where the number 67.38 and the number 1.026 were obtained.

Submitted: 123 days and 10 hours ago.

Category: Math

Value: $9

Status: CLOSED

Accepted Answer

"t = 0" is "1980"

1980: P(0) = 67.38(1.026^0) = 67.38

1981: P(1) = 67.38(1.026^1) = 69.13188, or 69.13 (rounded)

1982: P(2) = 67.38(1.026^2) = 70.92930888..., or 70.93 (rounded)

1983: P(3) = 67.38(1.026^3) = 72.77347091..., or 72.77 (rounded)

1984: P(4) = 67.38(1.026^4) = 74.66558115..., or 74.66 (truncated)

1985: P(5) = 67.38(1.026^5) = 76.60688262..., or 76.60 (truncated)

1986: P(6) = 67.38(1.026^6) = 78.59866531..., or 78.59 (truncated)

Values should be rounded, rather than truncated. I don't know why you were given truncated values to "confirm".

explanation: The population at time t = 0 (that is, in 1980) way 67.39 million; the annualized growth rate was 2.6% a year.

Accepts:
Expert:	Elizabeth
Pos. Feedback:	99.6 %
Answered:	7/20/2009

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