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The annual tuition at a specific college was $20,500 in 2000, and $45,4120
in 2018. Let x be the year since 2000, and y be the tuition. Write an
equation that can be used to find the tuition y for x years after 2000. Use
your equation to estimate the tuition at this college in 2020.

Sagot :

Varshamittal029idn

y = 20500 + 24090(x - 1) can be used to find the tuition y for x years after 2000. The tuition at this college in 2020 was $5,02,300.

We assume that the rate of increase in the cost of tuition fee per year is linear and hence the tuition fees of subsequent years will be in an Arithmetic Progression. The formula for determining the nth term of an arithmetic sequence which is expressed as-

Tn = a + (n - 1)d

Where

a = first term of the sequence.

d = common difference.

n = number of terms in the sequence.

According to the question,

a = $20500 (amount in 2000)

From 2000 to 2018, the number of terms is 19, hence,

n = 19

Thus, T19 = 454120

Therefore,

4,54,120 = 20500 + (19 - 1)d

454120 - 20500 = 18d

18d = 433620

d = 433620/18

d = 24,090

Therefore, the equation that can be used to find the tuition y for x years after 2000, is as follows-

y = 20500 + 24090(x - 1)

Now, the number of terms between 2000 and 2020 is 21, hence

x = 21

y = 20500 + 24090(21 - 1)

y = 20500 + 481800

y = $502300

Therefore, the tuition at this college in 2020 was $5,02,300.

Learn more about Arithmetic progressions here-

https://brainly.com/question/24205483

#SPJ9

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