Question

One of the children bought their teacher a mathematical plant for the classroom windowsill. At the end of the first day it had increased its height by a factor of a half. At the end of the second day it had increased its height from the end of day 1 by a factor of a third. The class found that this pattern continued day after day. How many days did it take to grow to 10 times its original height? PLEASE HELP ITS A QUESTION DUE TOMMOROW

Answer 1

Answer:

  18 days

Step-by-step explanation:

Here's a short table of heights:

  day 0: height = 1

  day 1: height = 1 + (1/2)(1) = 3/2

  day 2: height = (3/2) + (1/3)(3/2) = 3/2 + 1/2 = 2

The pattern of heights is ...

  (day, height) = (0, 1), (1, 1.5), (2, 2)

The plant is growing 1/2 its original height each day, so we can write the equation ...

  h = 1 + d/2

We want to find the number of days (d) that result in a height of 10 (ten times the original height).

  10 = 1 + d/2

  9 = d/2 . . . . subtract 1

  18 = d . . . . . multiply by 2

It took 18 days for the plant to grow to 10 times its original height.