Question

human hair grows at a rate of about 6.849×10 to the -4th power centimeters per hour to 2.329×10 to the -2nd power centimeters per hour. The rate depend depends on gender, genetics age and health find the difference between the high and in the low end of the range express your answer and scientific notation do not round your answer

Answer 1

To find the difference between the high and low end of the range for hair growth rates, we need to subtract the lower rate from the higher rate.

Given:

• Lower hair growth rate: \( 6.849 \times 10^{-4} \) cm/hour
• Higher hair growth rate: \( 2.329 \times 10^{-2} \) cm/hour

First, convert the lower rate to the same exponent as the higher rate:

\[ 6.849 \times 10^{-4} , \text{cm/hour} = 0.0006849 , \text{cm/hour} \]

Now, convert the higher rate to have the same exponent:

\[ 2.329 \times 10^{-2} = 2.329 \times 10^{-2} , \text{cm/hour} \]

Now, we can align the lower value with the higher exponent:

\[ 6.849 \times 10^{-4} = 0.0006849 = 0.00006849 \times 10^{-2} \]

Now we can perform the subtraction:

\[ 2.329 \times 10^{-2} - 0.00006849 \times 10^{-2} = (2.329 - 0.00006849) \times 10^{-2} \]

Calculating the subtraction:

\[ 2.329 - 0.00006849 \approx 2.32893151 \text{ (approximately)} \]

Expressing this in scientific notation:

\[ 2.32893151 \times 10^{-2} \]

We can express this in the required scientific notation format, accurately as:

\[ 2.32893151 \times 10^{-2} \text{ cm/hour} \]

Thus, the difference in hair growth rates expressed in scientific notation is:

\[ 2.32893151 \times 10^{-2} \text{ cm/hour} \]