PLEASE SHOW STEPS I know the answers but need to know how to

PLEASE SHOW STEPS! I know the answers but need to know how to do them...

1. Find out how long it takes a $2700 investment to double if it is invested at 7% compounded monthly . Round to the nearest tenth of a year. Use the formula A= P(1+ (r/n)^nt

2. The value of a particular investment follows a pattern of exponential growth. In the year 2000, you invested money in a money market account. The value of your investment t years after 2000 is given by the exponential growth model A = 3100e^0.046t. When will the account be worth $3902?

3. Use Newton\'s Law of Cooling, T = C + (T0 - C)e^kt, to solve the problem A tub of ice cream initially has a temperature of 25°F. It is left to thaw in a room that has a temperature of 68°F. After 10 minutes, the temperature of the ice cream has risen to 35°F. After how many minutes will the temperature of the ice cream be 53°F?:

4. A radio transmission tower is 140 feet tall. How long should a guy wire be if it is to be attached 13 feet from the top and is to make an angle of 20° with the ground? Give your answer to the nearest tenth of a foot.

5. An object is attached to a coiled spring. The object is pulled down (negative direction from the rest position) and then released. Write an equation for the distance of the object from its rest position after t seconds.

amplitude = 8 cm; period = 5 seconds

Thank you!

Solution

1. A= p(1 + r/n)^{n t}

Here p=$2700

A= 2*2700=$5400

R= 7%=.07

n=12

5400=2700(1+.07/12)^{12 t}

2= (12.07/12)^12t

log 2= 12 t log(12.07/12)

t=9.9 yrs

2. A= 3100 e^{.046 t}

3902= 3100e^.046t

ln(3902/3100)= .046 t

T= 5yrs

In 2005 the account be worth $3902