Unit 4aLesson 6 Practice Problems

The coordinates of Q are (0, 35) and R are (1.5, 14). Which function represents the graph.

• $\ 35\cdot\ \left(2.5\right)^{1.5x}$

• $35\cdot\ \sqrt[1.5]{0.4}^x$

• $\ 35\ \cdot\ \left(\frac{0.4}{1.5}\right)^x$

• $35\cdot\ ^3\sqrt{0.4}\ ^x$

• $\ 35\ \cdot\ \left(\frac{2.5}{1.5}\right)^x$

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CCSS.HSF.LE.A.2

A medication has a half-life of 4 hours after it enters the bloodstream. A nurse administers a dose of 225 milligrams to a patient at noon.

Which equation represents the amount of medication left after h hours?

• $f\left(h\right)\ =\ 225\cdot\left(0.5\right)^{\frac{h}{4}}$

• $f\left(h\right)\ =\ 225\cdot\left(-0.5\right)^h$

• $f\left(h\right)\ =\ 225\cdot\left(4\ \frac{1}{2}\right)^h$

• $f\left(h\right)\ =\ 225\cdot\left(\frac{0.5}{4}\right)^h$

• $f\left(h\right)\ =\ 225\cdot\sqrt{0.5}^{4h}$

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CCSS.HSF.LE.A.2

At the beginning of the year a blogger had 200 subscribers. Since then, the number of subscribers has been doubling every 8 weeks.

Select ALL equations that represent the number of subscribers, S, in terms of w weeks since the beginning.

• $S\ =\ 200\cdot w^2$

• $S\ =\ 200\cdot2^{\frac{w}{8}}$

• $S\ =\ 200\ \cdot\left(\frac{2}{8}\right)^w$

• $S\ =\ 200\cdot\sqrt[8]{2}^w$

• $S\ =\ 200\cdot8^w$

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CCSS.HSF.LE.A.2

Select ALL equations that represent the revenue, r, as a function of m months.

• $r\left(m\right)=\ 72,000\left(1.25\right)^{\frac{m}{3}}$

• $r\left(m\right)\ =\ 72,000\cdot\sqrt[3]{1.25}^m$

• $r\left(m\right)=\ 72,000\left(1.25\right)^m$

• $r\left(m\right)=\ 72,000\left(1.25\right)^{6m}$

• $r\left(m\right)=\ 72,000\cdot\sqrt{1.25}^m$

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CCSS.HSF.LE.A.2

Select ALL equations that represent the weight, w, of a catfish, t weeks since it was first weighed.

• $w\left(t\right)\ =\ 0.3\cdot\left(1.25\right)^{\frac{t}{2}}$

• $w\left(t\right)\ =\ 0.3\cdot\sqrt{1.25}^t$

• $w\left(t\right)\ =\ 0.3\cdot\sqrt[4]{1.25}^t$

• $w\left(t\right)\ =\ 0.3\cdot\left(1.25\right)^{\frac{t}{4}}$

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CCSS.HSF.LE.A.2

• 3

• 73

• 25

• 8

An insect population is rapidly increasing by doubling every 15 days. If there were originally 100 insects, which equation represents the insects after d days?

• $f\left(h\right)\ =\ 100\cdot2^{15h}$

• $f\left(h\right)\ =\ 100\cdot\ \left(\frac{1}{2}\right)^h$

• $f\left(h\right)\ =\ 100\cdot2^{\frac{h}{15}}$

• $f\left(h\right)\ =\ 100\cdot30^h$

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CCSS.HSF.LE.A.2

In 2000 a country had a population of 12.8 thousand. By 2010 the population had increased by 13%. During that decade, the population can be reasonably modeled by an exponential function.

Write an equation to show the country's population p(d), in thousands of people, d decades since 2000.

• $p\left(d\right)\ =\ 12.8\left(1.13\right)^d$

• $p\left(d\right)\ =\ 12.8\left(0.13\right)^d$

• $p\left(d\right)\ =\ 12.8\ +\ 1.3d$

• $p\left(d\right)\ =\ 12.8+0.13^d$

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CCSS.HSF.LE.A.2

In 2000 a country had a population of 12.8 thousand. By 2010 the population had increased by 13%. During that decade, the population can be reasonably modeled by an exponential function.

Select ALL expressions that represent the country's population in 2003.

•  $p\left(d\right)\ =\ 12.8\left(1.13\right)^{\frac{3}{10}}$

•  $p\left(d\right)\ =\ 12.8\cdot\sqrt[10]{1.13}^3$

•  $p\left(d\right)\ =\ 12.8\cdot\sqrt[3]{1.13}^{10}$

•  $p\left(d\right)\ =\ 12.8\cdot\left(1.13\right)^{2003}$

•  $p\left(d\right)\ =\ 12.8\cdot\left(1.13\right)^{\frac{1}{3}}$ 

 $y=a\cdot b^x$ 

Write an equation for the graph in the form:

•  $y\ =\ 8\cdot\sqrt{2.25}^x$ 

•  $y\ =\ 8\cdot2.25^x$ 

•  $y\ =\ 8\ \cdot\left(2.25\right)^{\frac{x}{3}}$ 

•  $y\ =\ 8\cdot\left(0.44\right)^{\frac{x}{2}}$ 

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CCSS.HSF.LE.A.2