Find with proof the minimum possible k such that every subset of f1; 2; : : : ; 2022g of size k must contain at least two elemen
1 answer:
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Answer:
After 7.04 years the amount will reach $57,000 or more
Step-by-step explanation:
The rule of the compound interest is , where
- A is the new value
- P is the initial value
- r is the rate in decimal
- n is the period of the time
- t is the time
∵ A loan of $36,000 is made at 6.75% interest, compounded annually
∴ P = 36,000
∴ r = 6.75% = 6.75 ÷ 100 = 0.0675
∴ n = 1 ⇒ compounded annually
∵ The amount after t years will reach $57,000 or more
∴ A = 57,000
→ To find t substitute these values in the rule above
∵ 57,000 = 36,000
∴ 57,000 = 36,000
→ Divide both sides by 36,000
∵ =
→ Insert ㏒ in both sides
∴ ㏒( ) = ㏒
→ Remember ㏒ = n ㏒(
)
∵ ㏒( ) = <em>t</em> ㏒(1.0675)
→ Divide both sides by ㏒(1.0675)
∴ 7.035151337 = <em>t</em>
<em>∴ </em><em>t </em>≅ 7.04
∴ After 7.04 years the amount will reach $57,000 or more
First, you are going to want to get the terms to the same power of 10 in scientific notation. Realize that . Essentially, we have converted the
to a term with
. Now, we can subtract the values in each term that are not 10 as shown below:
Remember that we have to turn it back to scientific notation once we are done!
Our answer is the second choice, . (This is the closest answer to
.)
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