Suppose the population of a town is 17,400 and is growing 2% each year.

Mathematics

2 answers:

sveticcg [70]2 years ago

8 0

Answer: 20,532

Step-by-step explanation:

17,400(.02)=348

348(9)=3132

17,400+3132=20,532

svet-max [94.6K]2 years ago

6 0

Answer:

Step-by-step explanation:

This is an exponential growth function of the form:

$y=ab^x$ where a is the initial population and b is the growth rate. This could also be written as

$y=a(1+r)^x$ which is a bit more accurate. We'll use that one. r is the percent growth: 2% for us.

Filling in the formula:

$y=17400(1+.02)^x$ and then simplifying:

$y=17400(1.02)^x$

That's the model for this population. Filling in any number of years for x will give you the population y. Our time is 9 years:

$y=17400(1.02)^9$

Take care of the exponents first, giving us:

$y=17400(1.195092569)$ and then multiply to get

y = 20,794.6 or 20,794 people (since you can't have 6/10 of a person)

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Apply Crammer's Rule to find the solution to the following quations .2x + 3y = 1, 3x + y = 5

Bond [772]

Answer:

The solution to the equation system given is:

x = 2
y = -1

Step-by-step explanation:

First, we must know the equations given:

2x + 3y = 1
3x + y = 5

Following Crammer's Rule, we have the matrix form:

$\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] =\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}1\\5\end{array}\right]$

Now we solve using the determinants:

$x=\frac{\left[\begin{array}{ccc}1&3\\5&1\end{array}\right]}{\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] } =\frac{(1*1)-(5*3)}{(2*1)-(3*3)} = \frac{1-15}{2-9} =\frac{-14}{-7} = 2$

$y=\frac{\left[\begin{array}{ccc}2&1\\3&5\end{array}\right]}{\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] } =\frac{(2*5)-(3*1)}{(2*1)-(3*3)}=\frac{10-3}{2-9} =\frac{7}{-7}=-1$

Now, we can find the answer which is x= 2 and y= -1, we can replace these values in the equation to confirm the results are right, with the first equation: