Answer:
F(t) = -0.54(t - 12)² + 104
Explanation:
We know that C(t) = -0.30(t - 12)² + 40 and F(t) = 9/5C(t) + 32
Then, we can replace C(t) on the equation of F(t) to get
[tex]\begin{gathered} F(t)=\frac{9}{5}C(t)+32 \\ F(t)=\frac{9}{5}(-0.30(t-12)^2+40)+32 \\ F(t)=\frac{9}{5}(-0.30)(t-12)^2+\frac{9}{5}(40)+32 \\ F(t)=-0.54(t-12)^2+72+32 \\ F(t)=-0.54(t-12)^2+104 \end{gathered}[/tex]
Therefore, the new function F(t) is
F(t) = -0.54(t - 12)² + 104
