Question

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

Answer 1

Answer:

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

Step-by-step 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, $\frac{520}{520}$ × $0.88^{b}$ < $\frac{100}{520}$

         or, $0.88^{b}$ < $\frac{1}{5.2}$

         or, ㏒ ( $0.88^{b}$ ) < ㏒  ($\frac{1}{5.2}$)

         or, b× ㏒ 0.88 < ㏒  ($\frac{1}{5.2}$)

         or,  $\frac{log (\frac{1}{5.2}) }{log (0.88)}$   <  b

         or, 12.89 < b

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