Question

human hair grows at a rate of about 6.849 times 10^negative 4 cm per hour to 2.329 times 10^negative 2 cm per hour. the rate depends on gender, genetics, age, and health. find the difference between the high end and the low end of the range. express your answers in scientific notation. DO NOT round your answer

Answer 1

To find the difference between the high end and the low end of the hair growth rates given in scientific notation, we subtract the lower value from the higher value:

High end: \( 2.329 \times 10^{-2} \) cm/hour
Low end: \( 6.849 \times 10^{-4} \) cm/hour

To perform the subtraction, we first express both values with the same exponent. The high end value is already in \( 10^{-2} \), so we can convert the low end value:

\[
6.849 \times 10^{-4} \text{ can be expressed as } 0.06849 \times 10^{-2}
\]

Now both values are in terms of \( 10^{-2} \):

- High end: \( 2.329 \times 10^{-2} \)
- Low end: \( 0.06849 \times 10^{-2} \)

Now we perform the subtraction:

\[
2.329 \times 10^{-2} - 0.06849 \times 10^{-2} = (2.329 - 0.06849) \times 10^{-2}
\]

Calculating the subtraction:

\[
2.329 - 0.06849 = 2.26051
\]

Thus,

\[
2.26051 \times 10^{-2}
\]

Finally, we express this in scientific notation:

\[
2.26051 \times 10^{-2}
\]

So, the difference between the high end and the low end of the hair growth rates is

\(\mathbf{2.26051 \times 10^{-2}} \text{ cm/hour}\).