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?

We can't tell where you're stuck. Please show your work.Is this homework?

A=P(1+r/n)^nt
A=amount
P=principal
r=rate
n=number times interest is calculated per year
t=number of year

Oh ya you also need the formula A=Pe^rt

Thank you so much for help however I already know the formulas. Perhaps I should be more precise; the answer is looking for a $$$ input; how can you translate a compounding number into a specific year?

Quote:

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Originally Posted by Dmaze1003

Thank you so much for help however I already know the formulas. Perhaps I should be more precise; the answer is looking for a $$$ input; how can you translate a compounding number into a specific year?

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This part of information that they give you"v(t)= 75,000e^t/5" looks similar to calculating compound interest continuously, but in any case you need to know the rate of interest I feel like there is missing information?

No sir I def put the information correctly. I had somebody help me and they came up with 20%; I did the math and 2003 the number comes out to be $203,871.1371. I just dont understand how to translate that into the answer of "per year"... the equation is not linear therefore you cant simply divide it.

I came up with the 20% interest well 19.6%, anyhow I am stumped on the per year part?

Quote:

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Originally Posted by Dmaze1003

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?

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Formula for future value (continuous compounding) : A[e^(i*t)]
At 9%, when does $1 accumulate to $2?
1[e^(.09t)] = 2
.09t = LOG(2)
t = LOG(2) / .09 = 7.7016... about 7 3/4 years ; OK?