A model for consumers' response to advertising is given by the equation N(a)=2100+470ln(a) Where N(a) is the number of units sold, a is the amount spent on advertising, in thousands of dollars, & a≥1.

(a)5347 Units

(b)

(c)The maximum point of N(a)=470. The minimum point does not exist.

Step-by-step explanation:

a) How many units were sold after spending $1,000 on advertising?

N(a)=2100+470ln(a)

N(1000)=2100+470ln(1000)

           =2100+3246.6

           =5346.6 ≈ 5347 Units

b) We are required to find the derivative of N(a)

N(a)=2100+470ln(a)

c) Find the maximum and minimum values of  N(a) if they exist.

The maximum and/or minimum value of N(a) is the point at which the slope or derivative of N(a)=0.

Given that

The maximum point of N(a)=470. The minimum point does not exist.

5.25 ounces

step-by-step explanation:

divided 3/4 and 6

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is