The populations P (in thousands) of Orlando, Florida from 2000 through 2007 can be modeled by P = 1656.2e^kt

where t represents the year, with t =0 corresponding to 2000.

In 2005, the population of Orlando was about 1,940,000. (Source: U. S. Census Bureau)

(a) Find the value of k. Is the population increasing or decreasing? Explain.

(b) Use the model to find the populations of Orlando in 2010 and 2015. Are the results reasonable? Explain.

Explained below.

Step-by-step explanation:

The population model for Orlando, Florida from 2000 through 2007 is:

It is provided that, in 2005, the population of Orlando was about 1,940,000.

(a)

Compute the value of k as follows:

For year 2005, the value of t is 5.

Since the value of k is positive, the population is increasing.

(b)

Compute the populations of Orlando in 2010 as follows:

Compute the populations of Orlando in 2015 as follows:

Since the population increased exponentially from 2010 to 2015, yes the results are reasonable.

1.4

2.3

step-by-step explanation:

the formula for the constant of variation is

y= kx

divide each side by x

y/x =kx/x

y/x =k

we know a and y

1.   y/x = k

4/1 =4

check the other values to make sure they are the same

8/2 = 4   12/3 =4   and 16/4 =4  

the constant of variation is 4

2.   y/x = k

3/1 =3

check the other values to make sure they are the same

6/2 = 3   9/3 =3   and 12/4 =3  

the constant of variation is 3

93.8

step-by-step explanation:

lets say, first number = x

second number = 3x+7

total = 49

(x)+(3x+7)= 49

4x+7 = 49

4x = 42

x = 42/4

x= 10.5

x= 10.5

3x+7 = 3(10.5)+7 = 93.8

hope this