Find the present value of $30000 due 13 years later at 7.2%, compounded continuously

1.Find the present value of $30000 due 13 years later at 7.2%, compounded continuously. 

2.By Newton's Law of Cooling, the rate at which an object cools is directly proportional to the difference in temperature between the object and the surrounding medium. If a certain object cools from 125° to 100° in half an hour when surrounded by air at 75°, find its temperature at the end of another half hour.

3.The radioactive element carbon-14 has a half-life of 5750 years. The percentage of carbon-14 present in the remains of plants and animals can be used to determine age. How old is a skeleton that has lost 40% of its carbon-14?

Note: Do not round any numbers during your calculation.

4.Suppose $15500 is invested in an account for 5 years. Find the balance in the account if interest is compounded continuously at 4%.

5.Find the absolute maximum and absolute minimum values of the function below. If an absolute maximum or minimum does not exist, enter NONE.

f(x) = 5 - 6x2 - 2x3 on the closed interval [-3,1]

6.Consider the following.

f(x) = -14ln(82x)

Compute f '(x), then find the exact value of f ' (9).

7.Find the derivative.

f(x) = x3 • e6x

8.Find the equation of the line that is tangent to the graph of y = 4 - x2 at the point (-1 , 3).

9.Answer in the form: Ax + By + C = 0, where A, B and C are relatively prime integers and A > 0.

A=

B=

C=

10.Find  

11.Solve the folowing inequality and put the solution in interval notation:

3x + 3 < 14x + 14

Note: To enter  , type infinity / To enter - , type –infinity

12.Find the family of curves represented by the following differential equation. (Use c as an arbitrary constant.)

13.Find the accumulated present value of an investment over a 12-year period if there is a continuous money flow of $2600 per year and the current interest rate is 11%, compounded continuously.

Note: Do not use commas in your answer.

14.Find the area under the curve:

y = 4x + (2/x2) from x = 1 to x = 4

15.On 1990 (t = 0), the world use of natural gas was 75051 billion cubic feet, and the demand for natural gas was growing exponentially at the rate of 7% per year. If the demand continues to grow at this rate, how many cubic feet of natural gas will the world use from 1990 to 2013?

Note: Do not use commas in your answer.

16.Find the amount of a continuous money flow in which $200 per year is being invested at 6.5%, compounded continuously for 15 years.

17.Find the area between the two curves:

y = ex

y = (1/x)

on [2,3]

See attachment...