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:
3.b
i hope question 3.a. is 5^x ÷ 5^-3 = 5^5
3.a.
Answer:
No cheating: you’re starring in a movie w/ the last person saved in your camera roll and the last song you listened to is the title.
"let's go everywhere" the movie with taemin and taeyong sounds like something i would watch ♡ https://t.co/tGdUt7CKPc
Answer:Justin plans to spend $20 on sports cards. Regular cards cost $3.50 per pack and foil cards cost $4.50 per pack
number of packs of regular cards =r and the number of packs of foll cards = f
Cost of Regular card = 3.50
Cost of 'r' packs of regular card = 3.50r
Cost of Foil card = 4.50
Cost of 'f' packs of Foil card = 4.50f
Justin plans to spend $20 on sports cards so the sum of cost of regular and Foil cards should be less than or equal to 20
The inequality becomes
3.50r + 4.50f <= 20
This one is a bit more complicated but i believe the answer is -1/4
