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:
D) y=-1/2x+4
Step-by-step explanation:
D) y=-1/2x+4
In order to be parallel, it has to have the same slope (-1/2). Also, if you plug in (-2,5) for x and y, it does pass through those coordinates.
Answer:
Step-by-step explanation:
Divide each term by 
and simplify.
Hope this helps :)
<em>-ilovejiminssi♡</em>
3/2(x - 10 ) = 1/2 x + 5
expand by using distributive property
3/2 x - 15 = 1/2 x + 5
subtract (1/2 x ) on both sides
x - 15 = 5
add 15 on both sides
x = 20
answer
C. x = 20
Answer:
223.34 m/s
Step-by-step explanation:
Given :
Travel time = 11 :23 pm to 1:00 a. M = 1 hour 37 minutes = (60 + 37) = 97 minutes = (97 * 60) = 5820 seconds
Distance between Seattle and San Francisco is
807.7 miles (culled from the internet)
807.7 miles = 1299867.1 meters
Average speed = Distance covered / Time taken
Average speed = 1299867.1 m / 5820 s
Average speed = 223.34486
Average speed = 223.34 m/s
