Question

The value of a machine is expected to decrease at a linear rate over time.
Two data pointa indicate that the value of the machine at t=0 (time of purchase) is
$18,000 end its value in 1 year will equal $14,500.
(a) Determine the slope-intercept equation (Væmt + k) which relates the value V of
the machine to its age t.
(b) Interpret the meaning of the slope and V intercept.
(c) Solve for the t intercept and interpret its meaning.​

please give me complete solution of this Question

Answer 1

V = - 3500t + 18000

Step-by-step explanation:

We have to determine the slope-intercept equation of the variables V (the value of the machine in dollars) and t (the time spent in years).

(a) The two ordered pairs are (0,18000) and (1, 14500).

So, the equation will be

$\frac{V - 18000}{18000 - 14500} = \frac{t - 0}{0 - 1}$

⇒ V - 18000 = - 3500t

⇒ V = - 3500t + 18000 (Answer)

(b) Now, the slope in the above equation i.e. - 3500 is the rate of decrease of machine value in $ per year.

And the V-intercept 18000 gives the initial value of the machine. (Answer)

(c) The t-intercept will give

0 = - 3500t + 18000

⇒ t = 5.14 years.

This means the value of the machine will become zero after 5.14 years. (Answer)

Answer 2

Answer:

V = - 3500t + 18000

Step-by-step explanation:

We have to determine the slope-intercept equation of the variables V (the value of the machine in dollars) and t (the time spent in years).

(a) The two ordered pairs are (0,18000) and (1, 14500).

So, the equation will be

\frac{V - 18000}{18000 - 14500} = \frac{t - 0}{0 - 1}

18000−14500

V−18000

=

0−1

t−0

⇒ V - 18000 = - 3500t

⇒ V = - 3500t + 18000 (Answer)

(b) Now, the slope in the above equation i.e. - 3500 is the rate of decrease of machine value in $ per year.

And the V-intercept 18000 gives the initial value of the machine. (Answer)

(c) The t-intercept will give

0 = - 3500t + 18000

⇒ t = 5.14 years.

This means the value of the machine will become zero after 5.14 years. (Answer)