Answer: 40k⁶-15k⁴
Step-by-step explanation:
To help Carmen find the total after 3 years
We'll have to use the annual compound interest formula: A = P(1 + r)ⁿ
A = Final balance (?)
P = Principal balance (6000)
r = Rate (0.028)
n = years (3)
A = 6000(1 + 0.028)³
A = 6000(1.028)³
A = 6000(1.086373952)
A = 6518.243712
Round that to the nearest cent, and we get $<u>6,518.24 </u>as the answer.
Pat attention to the ending of the numbers. If there are an odd amount of odds, it's going to be odd. If there is an even amount of odds, it's going to be even. If there's only evens, it's only going to stay even.
U(x) = f(x).(gx)
v(x) = f(x) / g(x)
Use chain rule to find u(x) and v(x).
u '(x) = f '(x) g(x) + f(x) g'(x)
v ' (x) = [f '(x) g(x) - f(x) g(x)] / [g(x)]^2
The functions given are piecewise.
You need to use the pieces that include the point x = 1.
You can calculate f '(x) and g '(x) at x =1, as the slopes of the lines that define each function.
And the slopes can be calculated graphycally as run / rise of each graph, around the given point.
f '(x) = slope of f (x); at x = 1, f '(1) = run / rise = 1/1 = 1
g '(x) = slope of g(x); at x = 1, g '(1) = run / rise = 1.5/ 1 = 1.5
You also need f (1) = 1 and g(1) = 2
Then:
u '(1) = f '(1) g(1) + f(1) g'(1) = 1*2 + 1*1.5 = 2 + 1.5 = 3.5
v ' (x) = [f '(1) g(1) - f(1) g(1)] / [g(1)]^2 = [1*2 - 1*1.5] / (2)^2 = [2-1.5]/4 =
= 0.5/4 = 0.125
Answers:
u '(1) = 3.5
v '(1) = 0.125
