Answer:
See Below
Step-by-step explanation:
The question is asking:
After how many years, 20,000 will become 500,000 at an annual interest of 11.5%?
So, we need compound growth formula shown below to solve this:
F is future value
P is present amount
r is rate of interest
t is the time of year
Given,
F = 500,000
P = 20,000
r = 11.5% = 11.5/100 = 0.115
t is what we want to find
Now, we take natural log of both sides and solve for t:
Its is going to take about 29.57 years, rounding, 30 years
Answer:
Step-by-step explanation:
We have to see how the canonical vectors are transformed throught T. Lets first define T in any basis.
Since T is a reflection, then any element of the line y = x/2 if fixed by T. Therefore T(2,1) = (2,1).
On the other hand, any vector perpendicular to the line direction should be sent to its opposite value. We can take, for example, (-1,2) (note that the scalar product (2,1) * (-1,2) = -2+2 = 0). As a consecuence T(-1,2) = (1,-2). We have
By summing the first vector with the double of the second one we get, using linearity
T(0,5) = T( (2,1) + 2(-1,2)) = T(2,1) + 2T(-1,2) = (2,1) + 2(1,-2) = (4,-3)
Hence, T(0,1) = (4/5,-3/5)
Now, we take the second vector and substract it the double of the first one (to kill the second variable)
T(-3,0) = T( (-1,2) - 2*(2,1) ) = T(-1,2) -2T(2,1) = (1,-2)-2(2,1) = (-3,-4)
Therefore, T(1,0) = (1,4/3)
The matrix A induced by T has in its first column T(1,0) and in its second column T(0,1). We conclude that