A wooden artifact from an ancient tomb contains 40 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

The exponential model \( A=177.2 e^{0.013 t} \) describe the population, \( A_{1} \) of a country in millions, \( t \) years after 2003 . Use the model to answer the following questions: a) what was the population of the country in 2003 ? b) By what percentage is the papulation of the country increasing each year?

Graph \( m(w)=-2 \cdot 2^{w} \)

Complete the sentence below. Suppose that the graph of a function \( f \) is known. Then the graph of \( y=f(-x) \) may be obtained by a reflection about the -axis of the graph of the function \( y=f(x) \). Suppose that the graph of a function \( f \) is known. Then the graph of \( y=f(-x) \) may be obtained by a reflection about the -axis of the graph of the function \( y=f(x) \).

Given two points for an exponential function, 1. Use the two points to find the growth rate, k . Write an exponential model for each point, then solve this system of two equations for k . 2. Use either point with the k you found to find the initial amount at time zero, \( \mathrm{A}_{\mathrm{o}} \). 3. Doubling time is when the amount is \( 2^{*} \mathrm{~A}_{\mathrm{o}} \). 4. Use the values of k and \( \mathrm{A}_{\mathrm{o}} \) to calculate the amount for a given time or to find the time to reach a specific amount in the future. The count in a bacteria culture was 600 after 20 minutes and 1900 after 30 minutes. Assuming the count grows exponentially. You may enter the exact value or round to 2 decimal places. What was the initial size of the culture? Find the doubling period. Find the population after 105 minutes. When will the population reach 14000 .

Given: \( f(x)=2\left(x^{2}-1\right) \) Sketch function \( f \) on the diagram sheet. Clearly show all intercepts with the axes.