Question

I'm having a problem with the last part of this logarithmic equations I will upload a photo

Answer 1

SOLUTION

For the last part

In how many months does the average score drops below 77

From the function

$f(x)=88-10\log (t+1)$

f(x) becomes 77, then we equate it and find the value of t.

So this becomes

$\begin{gathered} f(x)=88-10\log (t+1) \\ \\ 77=88-10\log (t+1) \end{gathered}$

We have

$\begin{gathered} 77=88-10\log (t+1) \\ \\ -11=-10\log (t+1) \\ \\ 11=10\log (t+1) \\ \\ \log (t+1)=\frac{11}{10} \\ \\ \log (t+1)=1.1 \end{gathered}$

Changing logarithmic form to index form we have

$\begin{gathered} t+1=10^{1.1} \\ \\ t=12.589-1 \\ \\ t=11.589 \end{gathered}$

The answer is 11.6 months to 1 d.p