(a) The growth of three dierent towns is described below. For each town, find a
ID: 3373671 • Letter: #
Question
(a) The growth of three dierent towns is described below. For each town, find a formula for a function
P(t) which gives the population of the town (in thousands of people) t years since the beginning of 1990.
i. Town A begins with 20,000 people in 1990 and grows by 3.5% from 1990 to 1991. The population
of Town A is growing linearly.
ii. Town B begins with 15,000 people in 1990. By the beginning of 1995, there are 15,600 people in Town B. The population of Town B is growing exponentially.
iii. Town C begins with 25,000 people in 1990 and is growing at a rate of 1,200 people per year.
At the beginning of 2000, after the closure of a large factory in town, the population of Town C starts decreasing at a constant percent rate of 6% per year.
(b) In 1990, Town B has a smaller population than Town A. Will Town B's population ever surpass
Town A's population? Explain why or why not.
Explanation / Answer
1.
(P-20000) = 1.035(t)
=>P= 20000+1.035t
2.
P = 15000e^(7.8t/1000)
3.
P= 37000*(0.94)^(t-10)
(b)
yes. because a has a linear growth, where as B has exponential growth which is faster
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