A town has a population of 13000 and grows at 4.5% every year. What will be the population after 13 years, to the nearest whole
2 answers:
Answer:
population after 13 years is around 23,039
Step-by-step explanation:
A town has a population of 13000 and grows at 4.5% every year.
Population growth is given by
y is the population after t years
'a' is the initial population= 13000
'r' is the rate of growth=4.5%= 0.045
t is the number of years=13
y=23,038.54
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Answer:
Step-by-step explanation:
We can use Part I of the Fundamental Theorem of Calculus:
Since we have two functions as the limits of integration, we can use one of the properties of integrals; the additivity rule.
The Additivity Rule for Integrals states that:
We can use this backward and break the integral into two parts. We can use any number for "b", but I will use 0 since it tends to make calculations simpler.
We want the variable to be the top limit of integration, so we can use the Order of Integration Rule to rewrite this.
The Order of Integration Rule states that:
We can use this rule to our advantage by flipping the limits of integration on the first integral and adding a negative sign.
Now we can take the derivative of the integrals by using the Fundamental Theorem of Calculus.
When taking the derivative of an integral, we can follow this notation:
- where u represents any function other than a variable
For the first term, replace with
, and apply the chain rule to the function. Do the same for the second term; replace
Simplify the expression by distributing and
inside their respective parentheses.
Rearrange the terms to be in order from the highest degree to the lowest degree.
This is the derivative of the given integral, and thus the solution to the problem.