IM Unit 4a - Algebra 2

In a pond, the area that is covered by algae doubles each week. When the algae was first spotted, the area it covered was about 15 square meters.

Which expression represents the area covered by algae 1 day after it was spotted.

• $15\ \cdot\ ^7\sqrt{2}$

• $15\ \cdot\ 2^1$

• $15\ \cdot\ 2^7$

• $15\ \cdot\ 2\ \left(\frac{1}{7}\right)$

• $15\ \cdot\frac{2}{7}$

The population of a city in thousands is modeled by the function below, where t  is the number of years after 2000.

 $f\left(t\right)\ =\ 175\ \cdot\ \left(1.04\right)^t$ 

Which of the following statements are true about the model.  Select ALL that apply. 

• The population in 2000 was 175
  

• The population in 2000 was 175,000

• The population grows by 4 percent each year

• The population in 1995 was 140,000

A bacteria population is tripling every hour.

By what factor does the population change in a half hour?

•  $\frac{3}{2}$  

•  $\sqrt{3}$  

•  $\frac{1}{3}$  

•  $\frac{2}{3}$  

•  $^{3\sqrt{\frac{1}{2}}}$  

Caffeine has an average half-life of about 5 hours. A man consumes an energy drink that contains 72 mg of caffeine. Which function represents the amount of caffeine left after h hours?

•  $72\cdot\left(\frac{1}{2}\right)^{5h}$  
  

•  $72\cdot\left(\frac{1}{2}\right)^h$  

•  $72\cdot\left(\frac{1}{2}\right)^{\frac{h}{5}}$  

•  $f\left(h\right)=72\cdot\left(\frac{1}{2}\right)^{\sqrt{h}}$  

•  $72\cdot\frac{1}{5}\cdot\left(\frac{1}{2}\right)^h$  

The value of a truck decreases exponentially since its purchase. The two points on the graph shows the truck’s initial value and its value one decade afterward.

Write an expression to represent the truck's value 3 years after purchase.

• $\ 40,000\ \cdot\ \left(0.85\right)^3$

• $\ 40,000\ \cdot\ \left(0.75\right)^{\frac{3}{10}}$

• $\ 40,000\ \cdot\ \left(0.85\right)^{\frac{3}{10}}$

• $\ 40,000\ \cdot\ \left(0.75\right)^3$

• $\ 40,000\ \cdot\frac{1}{10}\left(0.85\right)^3$

A population is growing exponentially by a factor of 1.15 every 3 months. Select ALL the expressions that represent the monthly growth factor.

• $\frac{1.15}{3}$

• $3^{1.15}$

• $\sqrt{3}$

• $\left(1.15\right)^{\frac{1}{3}}$

• $^3\sqrt{1.15}$

The graph shows a vehicle's value when it is first purchased and it's value 2 years later. 

What expression represents the value of the vehicle t years after purchase.

• $27850\ \sqrt{1.205\ ^t}$

• $27850\ \sqrt{0.83\ ^t}$

• $27850\ \frac{0.83^{\ t}}{2}$

• $27850\ \frac{1.205^{\ t}}{2}$

Tuition at a public university was $24,000 in 2005. By 2008 the tuition had increased exponentially by 18%. Since then, it has followed the same trend.

Select all true statements about the growth in tuition.

• The tuition cost increased by 6% each year.

• The tuition cost roughly doubles in 4 years.

• The function
  
   $f\left(x\right)\ =\ 24,000\left(1.18\right)^1$ 
  
  represents the cost of tuition in 2008. 
  
  
  

• The expression  
  
   $1.18^{\frac{1}{3}}$  
  
  represents the annual growth rate. 
  

• The function   $24,000\left(1.18\right)^{10}$  represents the tuition cost in 2015.
  

A bank account is growing exponentially. At the beginning of 2010, the balance was $1,000. At the beginning of 2014, the balance was $1,325. What would be the account balance at the beginning of 2019?

• $1883.59

• $12587.61

• $2495.75

• $2185.76

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

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

• $35\cdot\ \sqrt[1.5]{0.4}^x$

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

• $35\cdot\ ^3\sqrt{0.4}\ ^x$

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