5 is to 7 as is to 49 is to 51
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)!!!
The answer is "<span>the number of times the account compounds interest</span>".
The general formula is the following:
wherein r is the interest rate compound each four months.
Since there is 3*4 months in a year, then each year we compute the interest Three time, there where the factor 3 comes.
Regarding dilation, it is found that:
1. The scale factor is of 6.45
2. The scale factor is of 1.4375.
3. the image will be smaller than the pre-image.
<h3>Dilation</h3>
A dilation is one type of transformation that is applied to images, in which the side lengths are multiplied by a constant called scale factor, changing the side lengths of the image.
In item a, the initial length was of 11 and the final length is of 71, hence the multiplier, which is the scale factor, is given as follows:
71/11 = 6.45.
In item b, the initial length was of 16 and the final length was of 23, hence the scale factor is given as follows:
23/16 = 1.4375.
For item 3, the multiplier is a number that is less than 1, meaning that the image is smaller than the pre-image.
More can be learned about dilation at brainly.com/question/3457976
#SPJ1
