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)!!!
Figure 4 is the image of the square LMNP after the translation.
<u>Step-by-step explanation:</u>
Let us see the coordinates of the pre image LMNP as,
L (-3,1)
M(-1,1)
N(-1,-1)
P(-3,-1)
after translation of (x,y) → (x+5, y -3) the coordinates of the image obtained as,
L'(2,-2)
M'(4,-2)
N'(4,-4)
P'(2,-4) which matches the image 4.
Lynne ran farther and by 7/8 miles
You can tell Lynne ran further because she ran 3 whole miles while shelly only ran 2 whole miles. Now you have to subtract to see how much Lynne had ran more.
You found a common denominator between 8 and 4. 4 can turn into 8. so you multiply 4x2 and 1x2 to get a mixed number of 2 2/8
Now you have to turn 3 1/8 because you cannot subtract 2/8 from 1/8. You can turn the fraction into 2 9/8 because there are 8 pieces in a whole.
2 9/8 - 2 2/8 = 0 7/8
Hope this helps! :)
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