Question

I need help ASAP. I'm not good with math.

Answer 1

Given:

The increase in pressure P is the linear function of the depth d.

$P(d)=0.445d+14.7$

The cost of dinner is $300 and $10 per students.

To find:

The initial value and rate of change and their interpretation.

Find the cost function C where n is the number of students.

Solution:

The slope intercept form of a linear function is

$f(x)=mx+b$          ...(i)

where, m is rate of change and b is y-intercept or initial value.

We have,

$P(d)=0.445d+14.7$        ...(ii)

From (i) and (ii), we get

$m=0.445,b=14.7$

The initial value is 14.7. It means, the pressure at sea level is 14.7 pounds psi.

Rate of change is 0.445. It means, the pressure is increasing by 0.445 pounds psi for every feet.

The cost of dinner is $300 and $10 per students.

Let C(n) be the total cost for dinner and n be the number of students.

Fixed cost = $300

Additional cost for 1 student = $10

Additional cost for n student = $10n

Now,

Total cost = Fixed cost + Additional cost

$C(n)=300+10n$

Therefore, the required cost function is $C(n)=300+10n$.