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 < 13/2
Step-by-step explanation:
Rearrange:
Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :
8*d-5-(6*d+8)<0
Step by step solution :
Step 1 :
1.1 Divide both sides by 2
d-(13/2) < 0
Solve Basic Inequality :
1.2 Add 13/2 to both sides
d < 13/2
Inequality Plot :
1.3 Inequality plot for
2.000 d - 13.000 < 0
Answer:
135°
Step-by-step explanation:
In a parallelogram the opposite angles are congruent, so
∠BCD = ∠BAD = 135°
Answer:
18% decrease
Step-by-step explanation:
- 7,500 - 6,125 = $1,375
- Set up a proportion:
- Cross multiply, then divide: 1375 × 100 = 137500, 137500 ÷ 7500 = 18 1/3
- 18 1/3% rounded = 18%
- It went down, so it is a decrease
I hope this helps!
Minus 5 from both sides so we have 3a=-19 now divide both sides by 3 so we have a=-6 1/3
