Can someone please help?

The population of Collin County, which follows the exponential growth model,

Anestetic [448]

Answer:

(a) k=0.06217

(b) $P=264036e^{0.06217t}$

(c) 556,755 is the population in 2012

Step-by-step explanation:

Population increased from 264,036 in 1990 to 491,675 in 2000.

Let assume , year 1990 as t=0

When t=0, population P = 264,036

When t=10, population P = 491,675

Exponential growth equation is P=P_0e^(kt)

$P_0$ is the initial population when t=0

So $P_0= 264,036$

When t=10, population P = 491,675

Plug in all the values and find out k

$491675 = 264036 e^{k*10}$

Divide both sides by 264036

$\frac{491675}{264036}=e^{k*10}$

To remove 'e' we take ln on both sides

$ln(\frac{491675}{264036})=lne^{10k}$

$ln(\frac{491675}{264036})=10kln(e)$

The value of ln(e) = 1

$ln(\frac{491675}{264036})=10k$

Divide both sides by 10

k=0.06217

Exponential growth equation is $P=P_0e^{kt}$

We know $P_0= 264,036$

Replace the value of k

$P=264036e^{0.06217t}$

Now , we find the population in 2012

For year 2012 , t= 12

So we plug on 12 for t and solve for P

$P=264036e^{0.06217*12}$

P = 556755.09504

556,755 is the population in 2012

4 0

3 years ago

HELP!! Is –41/2 equivalent to (–4)1/2? Why or why not?

Oliga [24]

No, they are not equivalent. The first term, -4 1/2 equals 4 whole units and one half unit. All negative. So it’s like you have someone 4 and 1/2 dollars.

The second term, (-4)1/2 means multiplying -4 times 1/2. Doing the multiplication for this gives you -4/2. Solving the division here is -2. It’s taking away 1/2 dollar 4 times.

I hope this helped. Happy to answer any questions you have.

8 0

3 years ago

Please help me, I have a test tomorrow! Attachment bellow:

katrin2010 [14]

Answer:

1. A 2. B

Step-by-step explanation:

Whatever happens to x must also happen to y.

For the first question, x is doubled, which means that the value of y is also doubled.

For the second question, if the value of x triples, then the value of y triples as well, which means that it would be multiplied by 3.

We can check to see if these two answers are true by inputting values into the equations.

For the first equation, let's use the example x = 2

y = 5(2)

y = 10

If the value if x doubled, it would become x = 4

y = 5(4)

y = 20

As you can see, when the value of x doubled from 2 to 4, the value of y also doubled from 10 to 20.

You can do something similar for the other equation.

8 0

3 years ago

If the coefficient of determination is 0.394, what percentage of the data about the regression line is unexplained

olga nikolaevna [1]

Answer:

The percentage [regression line is unexplained] = 60.6%

Step-by-step explanation:

Given:

Coefficient of determination = 0.394

Find:

The percentage [regression line is unexplained]

Computation:

Coefficient of determination = 0.394

Coefficient of determination = 39.4%

The percentage [regression line is unexplained] = 100% - Coefficient of determination

The percentage [regression line is unexplained] = 100% - 39.4%

The percentage [regression line is unexplained] = 60.6%

8 0

3 years ago

Show your work please

Radda [10]

Answer:

D.

Step-by-step explanation:

17% is the same as 0.17. 2/9=0.22. 0.25 doesn't need to be changed.

7 0

3 years ago