question archive 1-How much would you need to deposit in a bank account paying 6%annual interest compounded continuously so that at the end of 15 years you would have $21,000? 2- Suppose that a bank account that compounds interest continuously grows from $200to $232 in three years
1-How much would you need to deposit in a bank account paying 6%annual interest compounded continuously so that at the end of 15 years you would have $21,000? 2- Suppose that a bank account that compounds interest continuously grows from $200to $232 in three years
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1-How much would you need to deposit in a bank account paying 6%annual interest compounded continuously so that at the end of 15 years you would have $21,000?
2- Suppose that a bank account that compounds interest continuously grows from $200to $232 in three years. What annual interest rate is the bank paying?
3- Suppose a colony of bacteria has a continuous growth rate of 24% per hour. By what percent will the colony have grown after nine hours?
4- For the given point find the angle the radius of the unit circle ending at that point makes with the positive horizontal axis. Among the infinite number of possible correct solutions, choose the one with the smallest absolute value. (−3/2,1/2)
5- Suppose an ant walks counterclockwise on the unit circle from the point (0,1)to the endpoint of the radius that forms an angle of 8π/7 radians with the positive horizontal axis. How far has the ant walked?Enter the exact answer in terms of π.
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1.) Present value = Future value / { e ^rt}
Where present value = ?, Future value $21000, r = 6% and t = 15
Present value = $21,000 / 2.4596 = $8,537.96
2.) Present value = Future value / { e ^rt}
Where present value = 200, Future value $232, r = ?% and t = 3
200 = $232 / { e ^(r*3) }
By solving this we can get r = 4.95%
3.) Number of bacteria after 9 hours = e^rt
Where r = 0.24 and t = 9
e^0.24*9 = 8.671138
So, % growth = 100 * (8.671138 - 1)= 767.11%
4.) For this we can fit the triangle of 60 degree in second quadrant. So, remaining angle is 180-60 = 120 degree.
5.) Circumference of the circle is 2pie
So, 8π/7 is the 4/7th part of the circle. As ant is walking anti clockwise. the distance = 1 - 4/7 = 3/7
Walking = 2π * 3/7 = 6π/7
