I need help with growth rate exponential calculus problems

[Moso13]

I missed one calc class due to being sick and have to figure out this worksheet for the quiz. All help would be greatly appreciated. Thank you
1. If Q(t) has a monthly percentage growth rate of 2.0%, what it its yearly percentage growth rate if compounded monthly?


2. If Q(t) doubles in 3 years, what is its continuous growth rate?


The formulas for these problems I have
Q(t)= Qo(1+r)^t Percentage growth
Q(t)= Qo(1+r/n)^nt Multiple compounding
Q(t)=Qoe^kt Continuous growth

 

[Deleted member 4993]

I missed one calc class due to being sick and have to figure out this worksheet for the quiz. All help would be greatly appreciated. Thank you
1. If Q(t) has a monthly percentage growth rate of 2.0%, what it its yearly percentage growth rate if compounded monthly?


2. If Q(t) doubles in 3 years, what is its continuous growth rate?


The formulas for these problems I have
Q(t)= Qo(1+r)^t Percentage growth
Q(t)= Qo(1+r/n)^nt Multiple compounding
Q(t)=Qoe^kt Continuous growth

What are your thoughts?

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/announcement.php?f=33

 

[Moso13]

What are your thoughts?

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/announcement.php?f=33

I know I would use the formula Q(t)= Qo(1+r/n)^nt and I think that the r would be .2, but I have no idea where to go from there

 

[Harry_the_cat]

I missed one calc class due to being sick and have to figure out this worksheet for the quiz. All help would be greatly appreciated. Thank you
1. If Q(t) has a monthly percentage growth rate of 2.0%, what it its yearly percentage growth rate if compounded monthly?


2. If Q(t) doubles in 3 years, what is its continuous growth rate?


The formulas for these problems I have
Q(t)= Qo(1+r)^t Percentage growth
Q(t)= Qo(1+r/n)^nt Multiple compounding
Q(t)=Qoe^kt Continuous growth

1. If Q(t) has a monthly percentage growth rate of 2.0%, what it its yearly percentage growth rate if compounded monthly?

Ok, say you had $100. After one year at 2.0% interest per month compounded monthly you would have $\(\displaystyle 100*(1+ 0.02)^{12}\)

Let the yearly percentage growth rate be R (as a decimal not a percentage).

After one year you would have $\(\displaystyle 100*(1 + R)^1\).

So these two amounts must be equal. That is:

\(\displaystyle 100*(1+ 0.02)^{12} = 100*(1 + R)^1\)

The 100s cancel, so you have:

\(\displaystyle (1+ 0.02)^{12} = 1 + R\)

You can now easily find R and convert it to a percentage by multiplying by 100.

 

[Harry_the_cat]

2. If Q(t) doubles in 3 years, what is its continuous growth rate?


Q(t)=Qoe^kt Continuous growth

Ok, so you need to find k.

\(\displaystyle Q_0 \) is your original amount.

So if it doubles in 3 years you will have:

\(\displaystyle 2*Q_0 = Q_0 * e^{3k}\)........................2* for "double" when t=3

Cancel the \(\displaystyle Q_0\).

Use natural log to find k.