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
