Question

If a = 4b + 5 and b = 1/4^x for x = 2, 3, or 4, what is the least possible value of a ?a) 4b) 5 1/64c) 5 1/4d) 69

Answer 1

The first step we need to do is substitute the value of 'b' in the expression of 'a':

`\begin{gathered} a=4b+5 \\ a=4((1)/(4)^{})^x+5 \end{gathered}`

Now, we just need to apply the values of x given and find what is the least possible value of 'a':

`\begin{gathered} x=2\colon \\ a=4((1)/(4))^2+5 \\ a=(4)/(16)+5=5\text{ 1/4} \\ \\ x=3\colon \\ a=4((1)/(4))^3+5 \\ a=(4)/(64)+5=5\text{ 1/16} \\ \\ x=4\colon \\ a=4((1)/(4))^4+5 \\ a=(4)/(256)+5=5\text{ 1/64} \end{gathered}`

(x=2:

a = 4(1/4)^2 + 5

a = 4/16 + 5 = 5 1/4

x=3:

a = 4(1/4)^3 + 5

a = 4/64 + 5 = 5 1/16

x=4:

a = 4(1/4)^4 + 5

a = 4/256 + 5 = 5 1/64)

The least possible value of those 3 is the value a = 5 1/64

So the correct option is B.