Seed Problem: The height of an amazing plant grown from a seed varies linearly with the time it has been in the ground. After six days it is 6cm tall and after 60 days it is 15.8m (1580 cm) tall.

1. Write the particular equation giving the height as a function of time.
2. Find the intercepts and explain them.
3. What would be the height in one year?
4. How long would it take for the plant to grow to a height of 1km?

Sincerely,
Julie

Hi Julie

If y is the height of the plant and x is the time the seed has been in the ground then the problem says that y varies linearly with x. That means that for some numbers a and b, y = ax + b. Since y=6 cm when x=6 days, 6=6a+b. Also since y=1580 cm when x=60 days, 1580=60a+b. This gives you two equations for a and b,
6=6a+b, and
1580=60a+b.

You should now be able to solve these equation to find a and b which gives the equation required in part 1.

Cheers
Penny