Please help me with these 2 problems!

1. Complete the table for the time t necessary for P dollars to triple if interest is compounded continuously at rate r.

r= 2%, t=?
r= 4%, t=?
r= 6%. t=?
r= 8%, t=?
r= 10%, t=?
r= 12%, t=?

2. Draw a scatter plot of the data in the above exercise. Use the regression feature of a graphing utility to find a model for the data.

^^I have no clue what the regression feature is.

2% - 54.93

4% - 27.47
6% - 18.31
8% - 13.73
10% - 10.99
12% - 9.16

1. Table for the time t necessary for P dollars to triple:

| Interest Rate (r) | Time (t) |
|-------------------|----------|
| 2% | ??? |
| 4% | ??? |
| 6% | ??? |
| 8% | ??? |
| 10% | ??? |
| 12% | ??? |

Well, if you want to triple your money with a 2% interest rate, you might have to wait a while. We're talking "Jurassic Park" kind of time here, so pack your bags and prepare for a prehistoric adventure.

Now, at a 4% interest rate, things start to look a bit more promising. You could spend your time downloading a dating app for dinosaurs - that's how much time we're talking.

With a 6% interest rate, you've got time to watch all the "Star Wars" movies and still have time left to debate which one is the best.

At 8% interest, you'll be waiting just long enough to learn an exotic dance routine. May I suggest "The Macarena"? Trust me, everybody will be impressed.

With a 10% interest rate, you'll have plenty of time to become a champion hotdog eater. There's a future in competitive eating for you! Think of all the mustard you'll need.

And finally, at a whopping 12% interest rate, you'll have enough time to become an Olympic athlete in every single sport. You'll be the undisputed champion of the world!

2. Drawing a scatter plot and using the regression feature:

Well, let's say the scatter plot is like a little family of points, where each point is a sibling and the line of best fit is their wise old grandparent. The regression feature is like calling in a genealogist to analyze the family tree and find the perfect grandparent, er, line of best fit for the data.

But don't worry, if you're as lost as Waldo in a crowd, finding the regression feature can be easier than finding your way home. Many graphing calculators have this feature built-in. Just look for an option that says "regression" or "linreg" (short for linear regression).

Once you locate it, simply follow the prompts. Just remember not to talk too much about the scatter plot's family drama, the regression feature prefers to stay focused on the numbers!

Good luck plotting those points and finding the perfect model for your data! And remember, if all else fails, just add a red nose to your scatter plot and call it a Clown Plot!

Sure, I'd be happy to help!

1. To complete the table for the time t necessary for P dollars to triple if interest is compounded continuously at rate r, we can use the formula for continuous compound interest:

A = P * e^(rt),

where A is the final amount, P is the initial principal, r is the interest rate, and t is the time in years.

In this case, we want to find the time t required for the principal P to triple, which means the final amount A is equal to 3P. Plugging this into the formula, we get:

3P = P * e^(rt).

To solve for t, we can divide both sides of the equation by P and take the natural logarithm (ln) of both sides:

ln(3) = rt.

Dividing both sides by r, we can solve for t:

t = ln(3) / r.

To complete the table, you just need to plug in the given values of r and calculate t using the formula t = ln(3) / r.

2. To draw a scatter plot of the data and find a model using regression, you will need a graphing utility (such as a graphing calculator or computer software). The regression feature allows you to find a mathematical model that best fits the given data.

First, plot the data points from the table on a graph, where the x-axis represents the interest rate r and the y-axis represents the time t. Each data point will be a pair (r, t).

Once you have plotted the points, use the regression feature of your graphing utility to find a model for the data. The specific steps to perform regression analysis may vary depending on the graphing utility you are using. Usually, you will need to select the points and choose the regression type (linear, quadratic, exponential, etc.).

By performing regression, the graphing utility will calculate the best-fitting model for the data based on the selected regression type. The model can then be displayed on the graph, showing the trend or relationship between the interest rate and the time required for the principal to triple.

If you are unfamiliar with the regression feature or your graphing utility, I recommend consulting the user manual or searching for tutorials specific to your device or software.

1. To get the values of t you will need for your table, solve the equation

(1+r)^t = 3.00
Hint: use logs.
For r = 6%
(1.06)^t = 3
t = log 3/log 1.06 = 18.85 years

2. I don't have a graphing calculator/utility. There might be some online application you can use. The product of r and the tripling time will be nearly a constant. You should try fitting a relation
t = constant/r, instead of a straight-line fit.

2% = 68

4% = 56
6% = 49
8% = 38
10% = 29
12% = 16