Question

On what day will there be less than 100 left? following the equation y = 5000(0.5)x

Answer 1

The given expression is

`y=5000(0.5)^x`

To find the day, we have to evaluate the function where y < 100.

`\begin{gathered} 5000(0.5)^x<100 \\ (0.5)^x<(100)/(5000) \\ (0.5)^x<(1)/(50) \end{gathered}`

Then, apply a logarithm on each side

`\begin{gathered} \ln (0.5)^x<\ln ((1)/(50)) \\ x\cdot\ln (0.5)<\ln ((1)/(50)) \\ x<(\ln((1)/(50)))/(\ln(0.5)) \\ x<5.6 \end{gathered}`

Therefore, on day 5 it will be less than 100.