The population of a small town is represented by the formula
P = 12500(0.98) t where P is the number of people and t is time in years.
a) Is the town's population increasing or decreasing? Explain how you know.
b) What is the initial population of the town?
c) Determine the population of the town 10 years from now. Round answer to nearest whole person.
I tried to do these question idk what I’m doing wrong :/
(a) b^x is decreasing if b < 1
(b) recall that 0.98^0 = 1
(c) just plug in t=10
show your work and we can prolly tell where you are going wrong ...
(a) b^x is decreasing if b < 1
(b) recall that 0.98^0 = 1
(c) just plug in t=10
A.decreasing
B. 12500
C. 122500
Don't worry! I'm here to help you understand and solve these questions.
a) To determine whether the town's population is increasing or decreasing, we need to look at the formula: P = 12500(0.98)^t. Specifically, the term (0.98)^t.
In this formula, the base 0.98 represents the proportion of the population that remains each year. Since the base is less than 1, it means that each year, the population is decreasing by a certain percentage. Therefore, the population of the town is decreasing over time.
b) The initial population of the town can be found by substituting t = 0 into the formula: P = 12500(0.98)^0. Any number raised to the power of 0 equals 1, so we get P = 12500(1), which simplifies to P = 12500. Therefore, the initial population of the town is 12,500 people.
c) To determine the population of the town 10 years from now, we substitute t = 10 into the formula: P = 12500(0.98)^10. To calculate this, we need to evaluate the expression (0.98)^10 using a calculator. The result is approximately 11331.50. Rounding this to the nearest whole person would give us 11,332 people.
So, the population of the town 10 years from now is approximately 11,332 people.