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Answer :
Option C.the correct inequality is 12000(1.05)^n < 20000.
This problem deals with exponential growth.
Tuition increases are modeled by the formula [tex]P(1 + r)^n[/tex] ,
where P is the initial amount,
r is the rate of increase,
n is the number of years.
Given this year's tuition P = $12,000 and the rate r = 5% = 0.05, the formula becomes [tex]12000(1.05)^n.[/tex]
We need the tuition to stay under $20,000, so the inequality is:
[tex]C. 12000(1.05)^n < 20000[/tex]
This inequality will help us determine how many years n it will take until the tuition reaches $20,000.
The other options involve incorrect bases (like 0.05 or 0.95) or incorrect growth rates.
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Rewritten by : Barada
The inequality that can be used to solve for n is option B, 12000(0.95)^n < 20000.
To determine the inequality that represents the tuition being less than $20,000 over the next n years, we need to use the formula for compound interest: A = P(1 + r)^n, where A is the final amount, P is the initial amount, r is the interest rate, and n is the number of years.
Since we want the tuition to be less than $20,000, we set A < 20000 and plug in the given values: 20000 > 12000(1 + 0.05)^n. We can simplify this to 20000/12000 > (1.05)^n, or 1.6667 > (1.05)^n. We can then solve for n by taking the logarithm of both sides: log(1.6667) > n log(1.05), or n < log(1.6667)/log(1.05). This gives us n < 9.32. However, since we're looking for a whole number of years, we can round up to n < 10. Finally, we can rewrite the inequality as 12000(0.95)^n < 20000, which is equivalent to option B.
To learn more about inequality click here : brainly.com/question/20383699
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