Algebra
Question 1
arqs = a(r+s)
(ar)s = ars
(ab)r = arbr
\(\left(\frac{a}{b}\right)^r\)= \(\frac{a^r}{b^r}\) = arb-r
\(\left(\frac{a^r}{a^s}\right)\) = a (r-s)
\(\frac{x^a}{x^b}\) = x(a-b)
Question 2
Knowing the surface area of a sphere with radius r is 4\(\Pi\)
If the radius of the sphere quadrupled, the surface area would increase by a factor of 4. If the radius of the sphere increased by a factor of x, the surface area would increase by a factor of x.
Question 3
A = total accrued amount
P = principal amount
r = yearly interest rate
t = unit of time (years)
The general formula for the calculation of interest is the following : A = P (1 + rt)
1,000,000 = 3,000 (1 + 40r)
1,000,000 = 3,000 + 120,000r
997,000 = 120,000r
r = \(\frac{997}{120}\)
r = 8.308
Therefore, the yearly interest should be of 830.8% in order to obtain $1 million in 40 years, starting with $3,000 today.