Enter the exponential decay function using t (for time) as the independent variable to model the situation. Select the graph of the function. Enter the function's domain and
range. Then complete the explanation of what the y-intercept represents in the context of
the problem. If necessary, round to the nearest penny.
The value of a couch is decreasing at a rate of 6.3% per year. In 2007, the couch was worth
$1,232. Find the value of the couch in 2014.

The decay function is  

The graph is attached down

The domain is {t: t ≥ 0}

The range is {y: y > 0}

The y-intercept represents the initial value of the couch

The value of the couch in 2014 is $781.25 to the nearest penny

Step-by-step explanation:

The form of the decreasing exponential function is , where

∵ The value of a couch is decreasing at a rate of 6.3% per year

∴

∴ y represents the amount of money

∴ t represents the number of years

∴ r = 6.3% = 6.3/100 = 0.063

∵ In 2007, the couch was worth  $1,232

∴ The initial value is $1,232

∴ a = 1,232

∵ We need to find the value of the couch in 2014

∴ t = 2014 - 2007 = 7 years

→ Substitute the values of a, r, and t in the function above

∵ The decay function is  

∵

∴

∴ y(7) = 781.2460671

→ Round it to the nearest penny (2 d.p)

∴ y(7) = 781.25

∴ The value of the couch in 2014 is $781.25 to the nearest penny

∵ The y-intercept is the value of y at t = 0

∴ The y-intercept represents the initial value of the couch

→ The graph is attached down

→ The domain is {t: t ≥ 0}

→ The range is {y: y > 0}

=====================================

explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer