Question

The profit( in thousands ) that a company makes, t years after opening, can be found by: F(t) = 2t^2 - 6t -3

a) How many years after opening did the company’s profit switch from negative to positive? ( round to the nearest tenth)
b) How many years after opening was the company’s profit the lowest?
c) What was the company’s profit( in thousands of dollars) when it was the lowest? ( don’t use dollar signs in your answer)

Answer 1

a) After 4 years the profit will change from negative to positive.

b)after 4 years the profit will be lowest.

Because the equation is a quadratic equation so, it will be increasing.

c) after 4 years the profit will be 5.

Explanation:

a) After 1 year = 2(1) -6(1) -3

= 2-9

= -7

It's negative

After 2 years = 2(4) -6(2) -3

= 8-12-3

= -7

It's negative

After 3 years = 2(9) -6(3) -3

= 18 - 18 -3

= -3

It's negative

After 4 years = 2(16) -6(4) -3

= 32 -24-3

= 5

It's positive

After 4 years the profit will change from negative to positive

b) after 4 years the profit will be lowest.

Because the equation is a quadratic equation so, it will be increasing.

c) profit = 2(16) - 6(4) -3

= 32 -24 - 3

= 5

after 4 years the profit will be 5