Question

Write an equation to model each problem. Solve the equation.

Answer 1

Answer:

1) The equation of the temperature in function of the time is

T(t) = 12 - 2t, with t in hours

The temperature is -4F after 8 hours, so, at P.M.

2) 6.75 = 7.50r

Her rate of deductions is 10% a day.

Step-by-step explanation:

1) This problem can be modeled by a first order equation

T(t) = T(0) + rt

In which T(0) is the temperature at instant zero and r is the rate of growth(r>0) or decline(r<0).

Since at 12 noon, the temperature outside is 12F, T(0) = 12. The temperature drops at the steady rate of 2F an hour, so r = -2.

The equation of the temperature in function of the time is

T(t) = 12 - 2t, with t in hours

The temperature is -4F when

-4 = 12 - 2t

2t = 16

t = 8h

The temperature is -4F after 8 hours, so, at P.M.

2) This problem can be modeled by the following first order equation

P = rP(0).

Where P is her pay, r is the rate of the initial money that Zelly takes home and P(0) is her initial pay.

In hour problem, we have that P = $6.75 and P(0) = $7.50.

So

6.75 = 7.50r

$r = \frac{6.75}{7.50}$

$r = 0.9$

r = 0.9 means that Zelly keeps 90% of her pay. It means that her rate of deductions is 10% a day.