Question

Please help me solve this im not really sure how:( I’ve been trying no luck

Answer 1

Solution:

Given the average score model;

$f(t)=85-6\log_{10}(t+1)$

On the original exam;

$\begin{gathered} t=0 \\ \\ f(0)=85-6\log_{10}1 \\ \\ f(0)=85 \end{gathered}$

His average score on the original exam is 85

(b) After one year;

$\begin{gathered} t=12 \\ \\ f(12)=85-6\log_{10}(12+1) \\ \\ f(12)=78.3 \\ \\ f(12)\approx78 \end{gathered}$

His average score after one year is 78

(c)

$\begin{gathered} f(t)=80 \\ \\ 80=85-6\log_{10}(t+1) \\ \\ \frac{-5}{-6}=\log_{10}(t+1) \\ \\ t+1=10^{(\frac{5}{6})} \\ \\ t=6.81-1 \\ \\ t=5.81 \end{gathered}$