Pre Calculus Questions & Answers

5. A research student is working with a culture of bacteria that doubles in size every 90 minutes. The initial population count was 1225 bacteria. Rounding to five decimal places, write an exponential function, \( P(t)=P_{0} e^{k t} \), representing this situation. To the nearest whole number, what is the population size after 5 hours?

5. a) Graph the function \( f(x)=-2(x-3)^{2}+4 \), and state its domain and range. \( D=\{x \in \mathbb{R}\} R=\{y \in \mathbb{R} \mid \) b) What does \( f(1) \) represent on the graph? Indicate, on the graph, how you would find \( f(1) \).

\[ f(x)=5(0.2)^{x} \] \( O a=0.2 ; b=5 ; \) exponential growth \( O a=5 ; b=0.2 ; \) exponential growth \( O a=5 ; b=0.2 ; \) exponential decay \( O_{a}=0.2 ; b=5 ; \) exponential decay

Determine whether the function below represents exponential growth or exponential decay. \[ y=12 \cdot\left(\frac{17}{10}\right)^{x} \]

Use transformations of the graph of \( f(x)=2^{x} \) to graph the given function. Be sure to graph and give the equation of the asymptote. Use the graph to determine the function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs. \( h(x)=2^{x-2}-1 \) Graph \( h(x)=2^{x-2}-1 \) and its asymptote. Graph the asymptote as a dashed line. Use the graphing tool to graph the function.

Determine whether the function below represents exponential growth or exponential decay. \[ \begin{array}{l}\text { (Hint: 1st identify which part of your function determines if you have a growth or decay.) } \\ \qquad y=2 \cdot(0.75)^{x}\end{array} \]

5. Dada la función exponencial \( h(x)=e^{\wedge}(2 x) \), ¿cuál es el valor de \( h(1) \) ? \( h(1)=e / 2 \) \( h(1)=e \) \( h(1)=2 e \)

Begin by graphing \( f(x)=3^{x} \). Then use transformations of this graph to graph the given function. Be sure to graph and give the equation of the asymptote. Use the graph to determine the function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs. \( g(x)=3^{x}-1 \) B. The graph of \( f(x)=3^{x} \) should be shifted 1 unit upward. C. The graph of \( f(x)=3^{x} \) should be shifted 1 unit to the right. Graph \( g(x)=3^{x}-1 \) and its asymptote. Use the graphing tool to graph the function as a \( f(x)=3^{x} \) should be shifted 1 unit downward. solid curve and the asymptote as a dashed line. The equation of the asymptote for \( g(x)=3^{x}-1 \) is The . (Type an equation.)

Begin by graphing \( f(x)=3^{x} \). Then use transformations of this graph to graph the given function. Be sure to graph and give the equation of the asymptote. Use the graph to determine the function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs. \( g(x)=3^{x}-1 \) Which transformation is needed to graph the function \( g(x)=3^{x}-1 \) ? Choose the correct answer below. B. The graph of \( f(x)=3^{x} \) should be shifted 1 unit to the left. C. The graph of \( f(x)=3^{x} \) should be shifted 1 unit upward. D. The graph of \( f(x)=3^{x} \) should be shifted 1 unit downward.

Use transformations of the graph of \( f(x)=3^{x} \) to graph the given function. Be sure to graph and give the equation of the asymptote. Use the graph to determine the function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs. \( g(x)=3^{x-6} \) Graph \( g(x)=3^{x-6} \) and its asymptote. Use the graphing tool to graph the function as a solid curve and the asymptote as a dashed line. The equation of the asymptote for \( g(x)=3^{x-6} \) is \( y=0 \). (Type an equation.) The domain of \( g(x)=3^{x-6} \) is ( \( \left.-\infty, \infty\right) \). (Type your answer in interval notation.) The range of \( g(x)=3^{x-6} \) is \( \square \). (Type your answer in interval notation.)