Why doesnt an elephant smoke

solve the problem related to population growth.A city had a population of 23,900 in 2007 and a population of 25,100 in 2012.(a)

Finger [1]

Solution

a)

To find the exponential growth function, we apply the exponential growth formula which is

$N(t)=a(1+k)^t$

Where

$\begin{gathered} a\text{ is the }initial\text{ population} \\ k\text{ is the growth rate} \\ t\text{ is the number of time intervals} \end{gathered}$

Given that

$\begin{gathered} a=23,900 \\ N(5)=25,100 \\ t=2012-2007=5 \end{gathered}$

Substitute the variables into the exponential growth formula

$\begin{gathered} 25100=23900(1+k)^5 \\ \text{Divide both sides by 23,900} \\ \frac{25100}{23900}=\frac{23900(1+k)^5}{23900} \\ 1.05021=(1+k)^5^{} \\ \sqrt[5]{1.05021}=1+k \\ 1.00984=1+k \\ \text{Collect like terms} \\ k=1.00984-1 \\ k=0.00984 \end{gathered}$

Hence, the exponential growth function is

$\begin{gathered} N(t)=23900(1+0.00984)^t_{} \\ N(t)=23900(1.00984)^t \end{gathered}$

Hence, the exponential growth function is

$N(t)=23900(1.00984)^t$

b)

For the population of the city in 2022,

$\begin{gathered} t=2022-2007=15 \\ t=15 \end{gathered}$

Substitute for t into the exponential growth function

$\begin{gathered} N(t)=23900(1.00984)^t \\ N(15)=23900(1.00984)^{15} \\ N(15)=27700\text{ (nearest hundred)} \end{gathered}$

Hence, the population is 2022 is 27700 (nearest hundred)

8 0

1 year ago

The following argument claims to prove that the requirement that an equivalence relation be reflexive is redundant. In other wor

sergij07 [2.7K]

Answer:

2

If R is a relation that is transitive and symmetric, then R is reflexive on dom(R)={a∣(∃b)aRb}: if a∈dom(R), then there is b such that aRb, thus bRa by symmetry, so aRa by transitivity.

Note that if R is symmetric, then dom(R)=range(R)={b∣(∃a)aRb}.

Hence, to get an example of a relation R on a set A that is transitive and symmetric but not reflexive (on A), there has to be some a∈A which is not R-related to any b∈A. There are many examples of this:

A={0,1} and R={(0,0)},

not reflexive on A because (1,1)∉R,

A={0,1,2} and R={(0,0),(0,1),(1,0),(1,1)},

not reflexive on A because (2,2)∉R.

Step-by-step explanation:

6 0

3 years ago

What is 16x60 and how

Greeley [361]

16x60=960
hope i helped

6 0

4 years ago

Read 2 more answers

Can someone please help me with this on ill mark you brainiest if correct

trapecia [35]

Answer:

We cannot find the 3rd Side unless & until the perimeter of triangle is not given!

5 0

3 years ago

Read 2 more answers

Hugh bought some magazines that cost $ 3.95 each and some books that cost $ 8.95 each. I have spent a total of $ 47.65. If Hugh

Alexxandr [17]

For how many books he got : 4

This is but adding up 3 of $3.95 to get the total of $11.85

You then want to subtract that from $47.65 to get $34.80

You subtract that by the $8.95 4 times so you see he bought 4 books

After you talk about how many books did he buy after that sentence I’m not sure what your saying

5 0

3 years ago