On his 13th birthday he was 112 cm tall and on his 14th birthday he was 121cm tall. Assume a geometric monthly growth rate. What is this rate? (%)
increase = 121-12 = 9
rate of increase = 9/112 = .08036
or appr 8%
that answer is wrong...
To find the geometric monthly growth rate, we need to use the formula:
Geometric growth rate = ((final value / initial value)^(1/n) - 1) * 100
In this case, the initial value is 112 cm, the final value is 121 cm, and the duration is 1 year (from the 13th to the 14th birthday), which is equivalent to 12 months. Therefore, n = 12.
Plugging in the values into the formula:
Geometric growth rate = ((121 / 112)^(1/12) - 1) * 100
Calculating the expression inside the bracket first:
(121 / 112)^(1/12) ≈ 1.00640
Substituting this value back into the formula:
Geometric growth rate ≈ (1.00640 - 1) * 100
Simplifying the expression:
Geometric growth rate ≈ 0.00640 * 100
Calculating the final result:
Geometric growth rate ≈ 0.64%
Therefore, the geometric monthly growth rate is approximately 0.64%.