SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

L&E, 2ADV E1 2024 HSC 13

The graph shows the populations of two different animals, and , in a conservation park over time. The -axis is the size of the population and the -axis is the number of years since 1985 .

Population is modelled by the equation  .

Population is modelled by the equation  .
 

Complete the table using the information provided.   (3 marks)

Show Answers Only

Show Worked Solution

Calculus, 2ADV C4 EQ-Bank 2

The population, , of Tasmanian Devils in a sanctuary is given by  , where    is the time in years after the sanctuary was established.

The devil population changes at a rate modelled by the function  .

Calculate the increase in the number of Tasmanian Devils at the end of the first 8 years. Give your answer correct to three significant figures.  (3 marks)

Show Answers Only

Show Worked Solution
 
 
 
 

L&E, 2ADV E1 SM-Bank 2

The population of Indian Myna birds in a suburb can be described by the exponential function

where is the time in months.

  1.  What will be the population after 2 years?  (1 mark)

  2.  Draw a graph of the population.  (2 marks)

Show Answers Only

  2.  

Show Worked Solution

i.   

 
 
 

 

ii.

Algebra, STD2 A4 2012 HSC 30c

In 2010, the city of Thagoras modelled the predicted population of the city using the equation

.

That year, the city introduced a policy to slow its population growth. The new predicted population was modelled using the equation

.

In both equations, is the predicted population and is the number of years after 2010.  

The graph shows the two predicted populations.
 

  1. Use the graph to find the predicted population of Thagoras in 2030 if the population policy had NOT been introduced.   (1 mark)

  2. In each of the two equations given, the value of is 3 000 000.

     

    What does represent?   (1 mark)

  3. The guess-and-check method is to be used to find the value of , in  .

     

    (1) Explain, with or without calculations, why 1.05 is not a suitable first estimate for .  (1 mark)

     

    (2) With    and  , use the guess-and-check method and the equation    to estimate the value of to two decimal places. Show at least TWO estimate values for , including calculations and conclusions.  (2 marks)

  4. The city of Thagoras was aiming to have a population under 7 000 000 in 2050. Does the model indicate that the city will achieve this aim?

     

    Justify your answer with suitable calculations.  (2 marks)

Show Answers Only
  1.  
  2.  
  3.  

     

Show Worked Solution

i.   

COMMENT: Common ADV/STD2 content in new syllabus.

 

ii.    


 

♦ Mean mark part (ii) 48%

iii. (1) 

   
 

iii. (2) 

 

 

 

 

 

iv.