16. Функцияны тақ-жұптыққа зерттеңіз: \( y=\frac{x^{3}+\sin 2 x}{\cos x} \) А) жұп B) тақ C) жалпы жағдайдағы функция D) Анықтау мумкін емес

Find the maximum \( y \)-value on the graph of \( y=f(x) \). \[ f(x)=-4 x^{2}+x-7 \] The maximum \( y \)-value is \( y=\square \). (Type an integer or a fraction.)

The function \( f(t)=60,000(2)^{\frac{1}{40}} \) gives the number of bacteria in a population \( t \) minutes after an initial observation. How much time, in minutes, does it take for the number of bacteria in the population to double?

Determine the implied domain of the following function. Express your answer in interval notation. \[ f(x)=\sqrt{x}-9 \] Answer

Use the remainder theorem to find the remainder when \( f(x) \) is divided by \( x-1 \). Then use the factor theorem to determine whether \( x-1 \) is a factor of \( f(x) \). \( f(x)=3 x^{3}-2 x^{2}+7 x-2 \) The remainder is \( \square \).

\( 1 \leftarrow \) Use the formula \( t=\frac{\ln 2}{\mathrm{k}} \) that gives the time for a population, with a growth rate k, to double, to answer the following questions. The growth model \( \mathrm{A}=9 e^{0.005 t} \) describes the population, A , of a country in millions, t years after 2003. a. What is the country's growth rate? \( \square \% \) b. How long will it take the country to double its population? \( \square \) years (Round to the nearest whole number.)