Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Connect with a community of experts ready to help you find accurate solutions to your questions quickly and efficiently. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

let x be the number of years since 2000, let y be the amount of money left in the fund that year. Use a linear equation to model the amount of money left in the fund after so many years.A)B)C)

Let X Be The Number Of Years Since 2000 Let Y Be The Amount Of Money Left In The Fund That Year Use A Linear Equation To Model The Amount Of Money Left In The F class=

Sagot :

a. The company spends $22,000 per year. Then, the amount of money left, decrease by $22,000 per year. In terms of the linear model, this means that the slope of the line is -22,000.

Equation of a line in slope-intercept form

[tex]y=mx+b[/tex]

where m is the slope and b is the y-intercept. In this case, the x-variable represents the number of years since 2000, and the y-variable represents the amount of money left in the fund.

In 2003, 3 years since 2000, there was still $852,000 left in the fund. This is equivalent to say when x = 3, y = 852,000. Substituting with these values and m = -22,000 into the equation, and solving for b:

[tex]\begin{gathered} 852000=-22000\cdot3+b \\ 852000=-66000+b \\ 852000+66000=b \\ 918000=b \end{gathered}[/tex]

And the equation of the linear model is:

[tex]y=-22000x+918000[/tex]

b. In the year 2009, x = 9. Substituting this value into the above equation and solving for y:

[tex]\begin{gathered} y=-22000\cdot9+918000 \\ y=-198000+918000 \\ y=720000 \end{gathered}[/tex]

There was $720,000 left in the fund

c. If the fund is empty, then y = 0. Substituting this value into the model's equation and solving for x:

[tex]\begin{gathered} 0=-22000x+918000 \\ 22000x=918000 \\ x=\frac{918000}{22000} \\ x\approx41.73 \end{gathered}[/tex]

At the end of the year 2041, the fund will be empty