1) 329 grams
2) 45 days
Explanations:The function representing the the number of grams present after t days is:
[tex]\begin{gathered} A(t)\text{ = }450e^{-0.04t} \\ \end{gathered}[/tex]To find the number of grams left after 8 days, substitute t = 8 into the function above:
[tex]\begin{gathered} A(8)=450e^{-0.04(8)} \\ A(8)=450e^{-0.32} \\ A(8)\text{ = }450(0.73) \\ A(8)\text{ = }328.5 \end{gathered}[/tex]A(8) = 329 (to the nearest whole number)
329 grams are left after 8 days
2) How long until 75 grams are left
That is, A(t) = 75
To get the value of t for A(t) = 75
[tex]\begin{gathered} 75=450e^{-0.04t} \\ \frac{75}{450}=\text{ }e^{-0.04t} \\ 0.167\text{ = }e^{-0.04t} \\ \ln \text{ 0.167 = -0.04t} \\ -1.79\text{ = -0.04t} \\ t\text{ = }\frac{-1.79}{-0.04} \\ t\text{ = }44.75 \\ t\text{ = 45} \end{gathered}[/tex]It will take 45 days for 75 grams to be left
