Draw the graph of \( f(x)=\log _{3}(x-3)+4 \)

A wooden artifact from an ancient tomb contains 30 percent of the carbon-14 that is present in living trees. How long ago, to the nearest year, was the artifact made? (The half-life of carbon-14 is 5730 years.) years

Which function transforms the translating it up 5 units? (1 point) \( g(x)=-2^{x+5} \) \( g(x)=2^{-x+5} \) \( g(x)=-2^{x}+5 \) \( g(x)=2^{-x}+5 \)

The fox population in a certain region has a continuous growth rate of 6 percent per year. It is estimated that the population in the year 2000 was 24200 . (a) Find a function that models the population \( t \) years after \( 2000(t=0 \) for 2000). Hint: Use an exponential function with base \( e \). Your answer is \( P(t)= \) (b) Use the function from part (a) to estimate the fox population in the year 2008 . Your answer is (the answer must be an integer)

Sketch a graph of the function \( f(x)=-3 \sin (3 x) \)

A population of bacteria is growing according to the equation \( P(t)=850 e^{0.03 t} \). Use a graphing calculator to estimate when the population will exceed 924. \( t=\square \) Give your answer accurate to one decimal place.