Answer:
2 * 10^3 = 2000.
Step-by-step explanation:
3.8/1.9 * 10^5/10^2
= 2 * 10^3
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:
Percentage increase in the cost of his train ticket = 3% (Approx.)
Step-by-step explanation:
Given:
Cost of annual ticket paid by Patrick last year = £2,534
Cost of annual ticket paid by Patrick current year = £2,612
Find:
Percentage increase in the cost of his train ticket
Computation:
Percentage increase = [(Current - Base) / Base]100
Percentage increase in the cost of his train ticket = [(2,612 - 2,534) / 2,534]100
Percentage increase in the cost of his train ticket = [(78) / 2,534]100
Percentage increase in the cost of his train ticket = [0.03078]100
Percentage increase in the cost of his train ticket = 3.078
Percentage increase in the cost of his train ticket = 3% (Approx.)
This is the answer for your question!
A) profit/original price x100 =percentage profit
(Profit: 360-300=$60)
=60/300 x100
=20%
b) two cameras (original price): 300x2= $600
two cameras (price sold): 360x2 = $720
Profit without discount: 720-600= $120
120-100= $20 discount
20/720 x100 =2.78%
