Subject: Seed Problem

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.

- Write the particular equation giving the height as a function of time.
- Find the intercepts and explain them.
- What would be the height in one year?
- 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

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