To find the difference between the high end and the low end of the range, we can subtract the lower growth rate from the upper growth rate.
Given:
- Lower growth rate: \( 6.849 \times 10^{-4} \) cm/hour
- Upper growth rate: \( 2.329 \times 10^{-2} \) cm/hour
First, we can convert the upper growth rate to the same power of ten as the lower growth rate for easier subtraction:
\[ 2.329 \times 10^{-2} , \text{cm/hour} = 2.329 \times 10^{-2} \times \frac{10^2}{10^2} = 232.9 \times 10^{0} , \text{cm/hour} = 232.9 \]
Now we want to convert \( 6.849 \times 10^{-4} \) to a decimal for easier calculation. It is already in scientific notation, representing:
\[ 0.0006849 \]
Now perform the subtraction:
\[ = 2.329 \times 10^{-2} , \text{cm/hour} - 6.849 \times 10^{-4} , \text{cm/hour} \] \[ = 0.02329 - 0.0006849 \]
Aligning the decimals for subtraction:
\[ \begin{array}{r} 0.0232900 \ -0.0006849 \ \hline 0.0226051 \end{array} \]
Converting \( 0.0226051 \) back into scientific notation:
\[ 0.0226051 = 2.26051 \times 10^{-2} \]
Thus, the difference between the high end and the low end of the range is:
\[ \boxed{2.26051 \times 10^{-2}} , \text{cm per hour} \]