Question 1204989
exponential equation is P = a * b ^ t
a would be equal to 20,000
b would be equal to 1 + .011 = 1.011
the equation would become P = 20,000 * 1.011 ^ t.
the equation can be graphed as shown below.


<img src = "http://theo.x10hosting.com/2023/111711.jpg">


in the graph, x takes the place of t.


at x = 0, the value is 20,000 * 1.011 ^ 0 = 20,000


at x = 1, the value is 20,000 * 1.011 ^ 1 = 20220


at x = 10, the value is 20,000 * 1.011 ^ 10 = 22312.157 rounded to 3 decimal places, as in the graph.


to create b, you take 1.1% and divide it by 100 to get .011.
that's the decimal equivalent of 1.1%.
you then add 1 to it to get 1.011.
that becomes the growth factor.


20,000 * 1.011 is the same as 20,000 + 20,000 * .011.
factor out the 20,000 and you get 20,000 * (1 + .011) which becomes 20,000 * 1.011.
for 1 year out, the value becomes 20,000 * 1.011.
for 2 years out, the value becomes 20,000 * 1.011 * 1.011 which is equal to 20,000 * 1.011^2
10 years out is 20,000 * 1.011^10