For a fixed rate, a fixed principal amount, and a fixed compounding cycle, the return is an exponential function of time. Using the formula, , let r = 10%, P = 1, and n = 1 and give the coordinates (t, A) for the points where t = 0, 1, 2, 3, 4. Round your answer to the hundredth's place.

Show coordinates and please explain the work. How would I show the graph?

Your y-axis would be the A (amount) or x-axis would be the t(time). Create a table of values using the formula and the given t's. Plot them on your graph. Make sure that you use an equivalent scale for each of the axis.

To find the coordinates (t, A) for the points where t = 0, 1, 2, 3, 4, we will use the formula for compound interest:

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

Given:
r = 10% (in decimal form, r = 0.10)
P = 1
n = 1 (compounding cycle is once per year)

We can now substitute the given values into the formula and calculate the corresponding values of A for each value of t:

When t = 0:
A = 1(1 + 0.10/1)^(1*0) = 1(1.10)^0 = 1(1) = 1
So, the first coordinate is (0, 1).

When t = 1:
A = 1(1 + 0.10/1)^(1*1) = 1(1.10)^1 = 1(1.10) = 1.10
The second coordinate is (1, 1.10).

When t = 2:
A = 1(1 + 0.10/1)^(1*2) = 1(1.10)^2 = 1(1.21) = 1.21
The third coordinate is (2, 1.21).

When t = 3:
A = 1(1 + 0.10/1)^(1*3) = 1(1.10)^3 = 1(1.331) = 1.331
The fourth coordinate is (3, 1.331).

When t = 4:
A = 1(1 + 0.10/1)^(1*4) = 1(1.10)^4 = 1(1.4641) = 1.4641
The fifth coordinate is (4, 1.4641).

Now we have the following coordinates:
(0, 1)
(1, 1.10)
(2, 1.21)
(3, 1.331)
(4, 1.4641)

To show the graph, you can plot these points on a coordinate plane. Choose the x-axis for time (t) and the y-axis for the amount (A). Create a table of values using the coordinates and mark the points on your graph. Make sure to use an equivalent scale for each of the axis, such as 1 unit per tick mark. Connect the plotted points smoothly to create the exponential curve that represents the growth of the amount over time.