Illustrative Math - Algebra 1 - Unit 5 -Lesson 10

A study was conducted to analyze the effects on deer population in a particular area. Let f be an exponential function that gives the population of deer  years after the study began.If f(t)=a*b^{t} and the population is increasing, select all statements that must be true.

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• {"blocks":[{"key":"0","text":"b<1","type":"unstyled","depth":0,"inlineStyleRanges":[],"entityRanges":[{"offset":0,"length":3,"key":0}],"data":{}}],"entityMap":{"0":{"type":"MATH","mutability":"MUTABLE","data":{}}}}
• {"blocks":[{"key":"0","text":"a>0","type":"unstyled","depth":0,"inlineStyleRanges":[],"entityRanges":[{"offset":0,"length":3,"key":0}],"data":{}}],"entityMap":{"0":{"type":"MATH","mutability":"MUTABLE","data":{}}}}
• The average rate of change from year 0 to year 5 is less than the average rate of change from year 10 to year 15.
• The average rate of change from year 0 to year 5 is greater than the average rate of change from year 10 to year 15.

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F.IF.6

A study was conducted to analyze the effects on deer population in a particular area. Let f be an exponential function that gives the population of deer  years after the study began.If f(t)=a*b^{t} and the population is increasing, select all statements that must be true.

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F.IF.6

Function models the population, in thousands, of a city years after 1930.The average rate of change of f from t=0 to t=70 is approximately 14 thousand people per year. Is this value a good way to describe the population change of the city over that time period? Explain or show your reasoning.

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F.IF.6

The function, f, gives the number of copies a book has sold w weeks after it was published. The equation f(w)=500*2^{w} defines this function.Select all domains for which the average rate of change could be a good measure for the number of books sold.

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• {"blocks":[{"key":"0","text":"0\\leq w\\leq7","type":"unstyled","depth":0,"inlineStyleRanges":[],"entityRanges":[{"offset":0,"length":12,"key":0}],"data":{}}],"entityMap":{"0":{"type":"MATH","mutability":"MUTABLE","data":{}}}}
• {"blocks":[{"key":"0","text":"5\\leq w\\leq7","type":"unstyled","depth":0,"inlineStyleRanges":[],"entityRanges":[{"offset":0,"length":12,"key":0}],"data":{}}],"entityMap":{"0":{"type":"MATH","mutability":"MUTABLE","data":{}}}}
• {"blocks":[{"key":"0","text":"5\\leq w\\leq10","type":"unstyled","depth":0,"inlineStyleRanges":[],"entityRanges":[{"offset":0,"length":13,"key":0}],"data":{}}],"entityMap":{"0":{"type":"MATH","mutability":"MUTABLE","data":{}}}}
• {"blocks":[{"key":"0","text":"0\\leq w\\leq10","type":"unstyled","depth":0,"inlineStyleRanges":[],"entityRanges":[{"offset":0,"length":13,"key":0}],"data":{}}],"entityMap":{"0":{"type":"MATH","mutability":"MUTABLE","data":{}}}}

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F.IF.6

The graph shows a bacteria population decreasing exponentially over time.The equation p=100,000,000*(\frac{2}{3})^{h} gives the size of a second population of bacteria, where is the number of hours since it was measured at 100 million. Which bacterial population decays more quickly? Explain how you know.

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F.IF.6

Give a value for r that would indicate that a line of best fit has a positive slope and models the data well.

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F.IF.6

The size of a district and the number of parks in it have a weak positive relationship.Explain what it means to have a weak positive relationship in this context.

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F.IF.6

Here is a graph of Han’s distance from home as he drives. Identify the intercepts of the graph and explain what they mean in terms of Han’s distance from home.

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F.IF.6