Assuming that Switzerland's population is growing exponentially at a continuous rate of 0.24 percent a year and that the 1988 population was 6.7 million, write an expression for the population as a function of time in years. (Let t=0 in 1988.)

Question

Barclay

Mathematics

15 January, 22:55

Assuming that Switzerland's population is growing exponentially at a continuous rate of 0.24 percent a year and that the 1988 population was 6.7 million, write an expression for the population as a function of time in years. (Let t=0 in 1988.)

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Missy · Answer 1

Answer:St = 6700000 (1 - 1.04^t) / 0.76

Step-by-step explanation:

Since the population is growing exponentially at a continuous rate of 0.24 percent a year, then a geometric progression is defined. The formula for the sum of n terms, Sn of a geometric progression is expressed as

Sn = a (r^n - 1) / r - 1

Where

a is the first term of the sequence

n is the number of terms

r is the common ratio

From the given information,

a = 6.7 million

r = 0.24

n = t

St = the population after t years

The expression for the population as a function of time in years will be

St = 6700000 (1.04^t - 1) / (0.24-1)

Since 0.24 is lesser than 1, it can be rewritten as

St = 6700000 (1 - 1.04^t) / (1 - 0.24)

St = 6700000 (1 - 1.04^t) / 0.76