The average daily high temperature (in \( \left.{ }^{\circ} \mathrm{C}\right) \) in Karachi, Pakistan, on the \( t^{\text {th }} \) day of the year is approximately \( T(t)=29-5 \cos \left(\frac{2 \pi(t-12)}{365}\right) \). What are the highest and lowest average daily highs in Karachi? Give exact answers. Highest: \( \square{ }^{\circ} \mathrm{C} \) Lowest: \( \square{ }^{\circ} \mathrm{C} \)

The elevation \( E \), in meters, above sea level at which the boiling point of a certain liquid is t degrees Celsius is given by the function shown below. At what elevation is the boiling point \( y=e^{t} \) where \( t=109.5^{\circ} \mathrm{C} \)

\( f(x)=\sqrt{4 x-x^{2}-3} \), con \( 2 \leq x \leq 3 \) a uno sobre su dominio respondencia \( f^{-1} \)

Sketch the graph of the exponential function \( g(x) = 3^{x-1} + 2 \), indicating its asymptote.

The population of a southern city follows the exponential law. Use this information to answer parts a and b . (a) If N is the population of the city and \( t \) is the time in years, express \( N \) as a function of t . \( \mathrm{N}(\mathrm{t})= \) (Type an expression using \( t \) as the variable and in terms of \( e \).) (b) If the population doubled in size over 14 months and the current population is 60,000 , what will the population be 4 years from now? The population will be approximately \( \square \) people. (Do not round until the final answer. Then round to the nearest whole number as needed.)

The elevation \( E \), in meters, above sea level at which the boiling point of a certain liquid is \( t \) degrees Celsius is given by the function shown below. At what elevation is the boiling point \( y=e^{t} \) where \( t=109.5^{\circ} \) Round your answer to the nearest tenths.