Question

The yearly profits of a new small business, in hundreds of dollars, during its first 10 years can be modeled by p(x) = x3 + x2 – 2x + 27, where x is the number of years since the business opened. What was the yearly profit in year 6

A.) $9300

B.) $14,100

C.) $7300

D.) $26,700

Answer 1

dso in year 6
for x=6

p(6)=6³+6²-2(6)+27
p(6)=216+36-12+27
p(6)=252+15
p(6)=267
in hundreds of dollars
time 100

267 times 100=26700


D is answer

Answer 2

Option D is correct

the yearly profit in year 6 is, $26,700

Explanation:

As per the statement:

The yearly profits of a new small business, in hundreds of dollars, during its first 10 years can be modeled as:

`p(x) =x^3+x^2-2x+27` ....[1]

where, x is the number of years.

We have to find the yearly profit in 6 years.

⇒
`x = 6`

Substitute in [1] we have;

`p(6) =6^3+6^2-2(6)+27`

⇒
`p(6)=216+36-12+27`

⇒
`p(6) = 267`

Since, p(x) represents the yearly profit in hundreds of dollars.

`p(6) = \$26, 700`

therefore, the yearly profit in year 6 is, $26,700