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)!!!
16, 24, 32, 40, 48, 56, 64, 72, etc.
The value of X = 10. A is the answer. You will equate the denominator by multiplying by the numerator and eventually you will get you answer which is 10
Answer:
The slope is 4
Step-by-step explanation:
First we pick 2 points (x, y):
(0, -2) and (1, 2)
Then, we use the slope (m) formula:
m = (y2 - y1)/(x2 - x1)
Given:
y2 = 2
y1 = -2
x2 = 1
x1 = 0
Work:
m = (y2 - y1)/(x2 - x1)
m = (2 + 2)/(1 - 0)
m = 4/1
m = 4
Answer:
Its the third one
Step-by-step explanation:
Plot all of the points onto the graph, and draw a line through all of the points. It most closely resembles the third one
