Find compounding interest & other problems

Hey all I'm completly new to this site and I have to say I am truly thrilled to find such a community. Here are my questions:

1. A painting purchased in 1998 for $75,000 is esitmated to be worth v(t)= 75,000e^t/5 dollars after t years. At what rate will the painting be appreciating in 2003?

In 2003, the painting will be appeciaiting at $____ per year.

2. Let P(t) be the population (in millions) of a certain city t years after 1990, and suppose thta P(t) satisfies the differential equation P'= .02(t), P(0)= 7.

a. Find the formula for P(t)

b. What was the initial popluation in 1990?

c. What is the growth constant?

d. What was the population in 2000?

e. Use the differential equation to determine how fast the population is growing when it reaches 8 million people.

f. How large is the population when it is growing at the rate of 190,000 people per year?

3. Suppose that an investment grows at a CONTINUOUS rate of 9% rate each year. In how many years will the value of the investment double?

Re: Find compounding interest & other problems

1.) You want to compute:

$\displaystyle \frac{dv}{dt}$

Then use the value for $\displaystyle t$ in 2003.

2.) You are given the IVP:

$\displaystyle \frac{dP}{dt}=0.02t$ where $\displaystyle P(0)=7$

a) solve the IVP.

b) You are given this as the initial condition.

c) The term growth constant is usually used with exponential growth, in my experience. This model is not exponential.

d) Using the result from part a), find P(10).

e) Using the result from part a), solve $\displaystyle P(t)=8$ for $\displaystyle t$, then use this in the ODE.

f) Use $\displaystyle P'(t)=0.19$ to find $\displaystyle t$, then use this in the solution from part a).

3.) Solve $\displaystyle 2=(1.09)^t$ for $\displaystyle t$.