Answer:
a) identity property of multiplication
b) commutative property in addition
R(t) = integral of r'(t) = integral of ti + e^tj + te^tk = 1/2t^2i + e^tj + (te^t - e^t)k + c
r(0) = j - k + c = i + j + k
c = i + 2k
Therefore, r(t) = (1/2t^2 + 1)i + e^tj + (te^t - e^t + 2)k
Answer:
<em>It will take 14 years before the investment triples</em>
Step-by-step explanation:
<u>Continuous Compounding</u>
Is the mathematical limit that compound interest can reach if it was calculated and reinvested into an account's balance over a theoretically infinite number of periods.
The formula for continuous compounding is derived from the formula for the future value of a compound interest investment:

Where:
FV = Future value of the investment
PV = Present value of the investment
i = Interest rate
t = Time
It's required to find the time for an investment to triple, that is, FV = 3 PV, knowing the interest rate is i=8%=0.08.
Substituting the known values:

Dividing by PV:

Taking logarithms:

Solving for t:


t = 13.7 years
Rounding up:
It will take 14 years before the investment triples