a) When a variable changes its value proportionally to its own value, like in this case, the model is exponential.
It can be exponential growth when the variable increases exponentially or exponential decay when it decreases exponentially.
In this case, it is a case of exponential decay, so this statement is false.
b) We can check the initial value of the amount for t = 0 and it is 500,000, so this statement is true.
c) We can check the amount after ten years as the amount for t = 10. We can do it as:
In the graph we can see that for t = 10, the amount is 300,000 so this statement is true.
d) Although the withdrawn percentage stays the same, the withdrawn amount is different each year.
For example, the first year will withdrawn $500,000 * 0.05 = 25,000.
The second year, the remaining amount is $475,000, and he will withdrawn a 5% of that: $475,000 * 0.05 = 23,750.
Then, this statement is false.
e) The y-intercept correspond to the amount at time t = 0, when no witdrawns have been made.
This statement is true.
Answer:
a) False
b) True
c) True
d) False
e) True