Question

An exponential model shows the growth of a towns population in years. Identify the parts:

y=25,000(1+.02)^12
Does this show growth or decay?
Rate(in %):
Starting Population:
Time:
Current Population:

Answer 1

9514 1404 393

Answer:

• 2% growth per year
• 25,000 to start
• 12 years
• 31,706 currently

Explanation:

The base of the exponent is (1 +0.02). The value 0.02 = 2% is the growth rate. It is positive, signifying a 2% rate of growth per year. (Negative values would mean decay.)

The number 25000 that multiplies the exponential term is the value of the expression when the exponent is zero. It represents the starting population.

The exponent is said to be in years, so the time is 12 years.

The current population is the value of the expression:

25,000(1.02^12) ≈ 31,706 . . . . current population