Determine results of

Question

In a science experiment, a student is studying the relationship between the temperature and the growth of a plant. She develops the following quadratic model: h=-0.0625t^2 +3t-20, where h is the height of plant, in cm, and t is growing of temperature, in Celsius

A. Determine the temperatures that result in a plant height of zero

B. Use your result from part a, to find the temperature that will maximize the height of the plant

C. Use this equation to determine the height of the plant grown at a temperature of 5 degrees Celsius. Comment on the domain of mathematical model. 

Answer 1

A)

 

Set h=0, and solve for x.

 

0 = -0.0625t² + 3t - 20

 

 

Use the quadratic formula

 

t = (-b ± √(b² - 4ac)) / 2a

 

where:

a = -0.0625

b = 3

c = -20

 

Plug in these values into the formula to get your t values.  You will get two values because of the plus/minus sign.  Since it asks for temperatures, you will accept both values of t.

 

 

B)

 

A quadratic function is a symmetrical one.  The maximum height occurs at the axis of symmetry.

 

Axis of symmetry is the average of the t values you obtained from the previous part.  Plug in the axis of symmetry into the function to obtain the maximum height.

 

 

C)

 

Evaluate h when t=5.   Since we have a quadratic function, the domain is all real numbers.  This means that from the interval  (-∞, axis of symmetry), the plant grows. 

 

In the interval (axis of symmetry, ∞), the plants begins to die.