Question

The height of a sunflower plant varies directly with its age. Once it has sprouted from the ground, when a sunflower is 2 week old, it is 38 centimeters tall. When it is 6 weeks old, it is 114 centimeters tall. How tall is a sunflower plant that is 3 1/2 weeks old? A. 47.5 cm, B. 57 cm, C. 66.5 cm, D. 76 cm

Answer 1

The speed of the growth will be equal to the distance travelled divided by time taken. Therefore, because 6-2 = 4 and 114 - 38 = 76, it increases by 76 centimetres every 4 weeks. The speed of growth is therefore 76 divided by 4 = 19.

So, every week it grows roughly 19 centimetres. To find out how much it grows in 3 1/2 weeks, simply multiply 19 by 3 1/2 which gives 66.5 cm. 

The answer is C, 66.5 cm.

Answer 2

Using direct variation formulas, y = k*x where y = 38 and x = 2.

k, the constant of direct variation here is 19  (38/2)

The formula for the sunflower growth is:

y = 19*x where x is the number of weeks and y is the height

At 3 1/2 weeks or 3.5 weeks, y = 19 * 3.5 = 66.5 cm height

Answer: C) 66.5 cm