The population of the country of oz was 600,000 in the year 2010. the population is expected to grow by a factor
of 5% annually. the annual food supply of oz is currently sufficient for a population of 700,000 people and is
increasing at a rate that will supply food for an additional 10,000 people per year.
c. at what point does the population exceed the food supply? justify your response.

After 5 years (2015)

Step-by-step explanation:

The population is increasing 5% per year, so the first year it will be 1.05 of the initial, the next year 1.05x1.05 of the initial, and then  successively, so, for n years:

P(n) = 600,000*(1.05)ⁿ

The food suply increase 10,000 people per year, so the first year will be 10,000 + the initial, the next year 10,000 + 10,000 + the initial, and then  successively, so, for n years:

F(n) = 70,000 + 10,000*n

So

P(n) > F(n)

600,000*(1.05)ⁿ > 70,000 + 10,000*n

(1.05)ⁿ > 1.167 + 0.0167n

Solving in a computer:

n > 4.42

So, after 5 years the population exceed the food supply.

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