Phil invested $150 at an annual rate of 4% compounded continuously, what amout to the nearest cent will be in his account after 2 years? Graph the amount in his account over the first 8 years.

P = Po*e^rt

Po = $150 = Initial investment.

rt = (4%/100%)/yr * 2yrs = 0.08.

Plug the above values into the given Eq
and get:
P = $162.49.

Use the following data for graphing:
(X,Y) or
(T,P).
(1,156.12).
(2,162.49).
(3,169.12).
(4,176.03).
(5,183.21).
(6,190.69).
(7,198.47).
(8,206.57).

To calculate the amount in Phil's account after 2 years with continuous compounding, we can use the formula:

A = P * e^(rt)

Where:
A = the amount in the account after time t
P = the principal amount (initial investment)
r = the annual interest rate (expressed as a decimal)
t = the time in years
e = Euler's number (approximately 2.71828)

Given:
P = $150
r = 4% = 0.04
t = 2 years

Plugging these values into the formula, we get:

A = 150 * e^(0.04 * 2)

Now, let's calculate the amount.

Step 1: Calculate the exponent.
0.04 * 2 = 0.08

Step 2: Multiply the exponent by Euler's number (e).
e^(0.08) ≈ 1.08328706767

Step 3: Multiply the result by the principal amount (P).
A = 150 * 1.08328706767

Rounding to the nearest cent, we find:
A ≈ $162.49

Therefore, the amount in Phil's account after 2 years will be approximately $162.49.

Next, let's graph the amount in his account over the first 8 years.

To graph the amount over time, we'll use the same formula repeatedly for each year, starting from year 0 to year 8.

The graph will have years on the x-axis and the amount in Phil's account on the y-axis.

Here's the table of values:

Year | Amount
---------------
0 | $150.00
1 | $156.71
2 | $162.49
3 | $168.47
4 | $174.65
5 | $181.04
6 | $187.65
7 | $194.48
8 | $201.55

Now, plot these points on a graph where the x-axis represents the years and the y-axis represents the amount in Phil's account, and connect them to create a smooth curve.