The population of a town is 20,000. It decreases at a rate of 9% per year. In about how many years will the population be fewer
than 14,000?
a. 1 year
b. 2 years
c. 3 years
d. 4 years
a. 1 year
b. 2 years
c. 3 years
d. 4 years
2 answers:
Answer:
d. 4 years
Step-by-step explanation:
A graphing calculator can be a real help with problems like this.
Or, you can write an explicit formula for the population and solve for the time it takes.
p = p0(1 +r)^t = 20,000(0.91^t) . . . . . . for r = -0.09, p0 = 20,000
Fill in p=14000, and divide by 20,000.
14000/20000 = 0.91^t
Take logarithms.
log(14/20) = t·log(0.91)
log(0.7)/log(0.91) = t ≈ 3.782
In 4 years, the town's population will be fewer than 14,000.
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Answer:
B - P=11.8(1.02)^t
Step-by-step explanation:
An exponential function is defined as:
.
Recall, a is the starting value, b is the rate, and x is the input (often time).
We will substitute a=11.8 million, b=1.02, and x=t for years. Notice b=1.02 and not 0.02. Because the population is increasing, we multiply by 1+r to add the growth onto the current population.
We write: where y is population in millions.