Answer:
Part a. t = 7.29 years.
Part b. t = 27.73 years.
Part c. p = $3894.00
Step-by-step explanation:
The formula for continuous compounding is: A = p*e^(rt); where A is the amount after compounding, p is the principle, e is the mathematical constant (2.718281), r is the rate of interest, and t is the time in years.
Part a. It is given that p = $2000, r = 2.5%, and A = $2400. In this part, t is unknown. Therefore: 2400 = 2000*e^(2.5t). This implies 1.2 = e^(0.025t). Taking natural logarithm on both sides yields ln(1.2) = ln(e^(0.025t)). A logarithmic property is that the power of the logarithmic expression can be shifted on the left side of the whole expression, thus multiplying it with the expression. Therefore, ln(1.2) = 0.025t*ln(e). Since ln(e) = 1, and making t the subject gives t = ln(1.2)/0.025. This means that t = 7.29 years (rounded to the nearest 2 decimal places)!!!
Part b. It is given that p = $2000, r = 2.5%, and A = $4000. In this part, t is unknown. Therefore: 4000 = 2000*e^(2.5t). This implies 2 = e^(0.025t). Taking natural logarithm on both sides yields ln(2) = ln(e^(0.025t)). A logarithmic property is that the power of the logarithmic expression can be shifted on the left side of the whole expression, thus multiplying it with the expression. Therefore, ln(2) = 0.025t*ln(e). Since ln(e) = 1, and making t the subject gives t = ln(2)/0.025. This means that t = 27.73 years (rounded to the nearest 2 decimal places)!!!
Part c. It is given that A = $5000, r = 2.5%, and t = 10 years. In this part, p is unknown. Therefore 5000 = p*e^(0.025*10). This implies 5000 = p*e^(0.25). Making p the subject gives p = 5000/e^0.25. This means that p = $3894.00(rounded to the nearest 2 decimal places)!!!
Answer:
THE ANSWER IS C
Step-by-step explanation:
BECAUSE BABABOOEEE
Answer:
40 points
Step-by-step explanation:
The score for the first four rounds of the game is 13, 17, 19, and 21 points.
Let 
and 
be the scores of the fifth and sixth games respectively in order to achieve an average score of 20 points per round for all six rounds.
Hence, the combined score of the fifth and sixth rounds are 40 points.
Answer:
A
Step-by-step explanation:
Melanie is correct
85 x 0.35 = 29.75
85 - 29.75 = 55.25
Answer: 20%
100 shares at $45each cost 100*45 = $4500
After a year, he sold the share at the rate if $52 each and it cost 52*100 = 5200
He received dividend of $2 on each dollars meaning 100*2 = $200
So,
$5200+200 = 5400
Profit = $5400 - 4500 = 900
%profit = 900*100 / 4500 = 20
