if something grows @ 10% per year how long would it take to go from 100 to 300?

need help with the setup on this problem.. if something grows @ 10%

the answer ie 30

thanks how would the set up go

300=100*(1.1)^t

(1.1)^t=3
t=ln3/ln(1.1)=11.53 years

Great thank you!

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the final amount
P = the initial amount (100 in this case)
r = the annual interest rate (10% in this case, which is written as 0.10)
t = the number of years we want to calculate
n = the number of compounding periods per year (assuming one compound per year, n = 1)

In this case, we want to find out how long it will take for the initial amount of 100 to grow to 300, with an annual interest rate of 10%.

So, we need to solve for t in the equation:

300 = 100(1 + 0.10/1)^(1t)

To solve for t, we can take the natural logarithm (ln) of both sides of the equation to eliminate the exponent:

ln(300) = ln(100(1 + 0.10/1)^(1t))

Next, we can use the logarithmic properties to simplify the equation:

ln(300) = ln(100) + ln(1.10^t)

Now, we isolate t by subtracting ln(100) from both sides of the equation:

ln(300) - ln(100) = ln(1.10^t)

Now we can simplify further by using the properties of logarithms:

ln(300/100) = t * ln(1.10)

Finally, we can isolate t by dividing both sides of the equation by ln(1.10):

t = ln(300/100) / ln(1.10)

Using a calculator, we can evaluate the right-hand side of the equation to find the value of t, which is approximately 16.38 years.

So, it would take approximately 16.38 years for the initial amount of 100 to grow to 300 at an annual interest rate of 10%.