Question

When will the equation p(b)=520(0.88)^b have a value less than 100?

Answer 1

The given equation will have value less than 100 whenever the value of b is greater than 12.89

Explanation:

For the given equation, p(b) = 520 ×
`0.88^(b)` to have a value less than 100 we can establish inequality as:

p(b) < 100

or, 520 ×
`0.88^(b)` < 100

or,
`(520)/(520)` ×
`0.88^(b)` <
`(100)/(520)`

or,
`0.88^(b)` <
`(1)/(5.2)`

or, ㏒ (
`0.88^(b)` ) < ㏒ (
`(1)/(5.2)`)

or, b× ㏒ 0.88 < ㏒ (
`(1)/(5.2)`)

or,
`(log ((1)/(5.2)) )/(log (0.88))` < b

or, 12.89 < b

Hence for the equation to have value less than 100, b must be greater than 12.89.