Answer:
Diverge
Step-by-step explanation:
(a)
1st year: [tex] 1000 * 1.08^1 = \$1080[/tex]
2nd year: [tex] 1000 * 1.08^2 = \$1166.4[/tex]
3rd year: [tex] 1000 * 1.08^3 = \$1259.71[/tex]
4th year: [tex] 1000 * 1.08^4 = \$1360.49[/tex]
5th year: [tex] 1000 * 1.08^5 = \$1469.33[/tex]
(b) The sequence is divergent, because if we take the derivative of the function with respect to n year:
[tex](1000*1.08^n)^{'} = 1000ln(n)*1.08^n[/tex]
This is a positive, meaning the slope of the function is positive. If we take the second derivative using product rule
[tex](1000ln(n)*1.08^n)^{'} = 1000\frac{ln(n)}{n}1.08^n[/tex]
This is also positive when n > 0. Therefore, the slope is positive and increasing. This means the sequence diverges.
