Question

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.)

Answer 1

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

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