a rock formation in a cave grows at a rate of 9×10^(-5) centimeter per year.\nhow much does the rock…

a rock formation in a cave grows at a rate of 9×10^(-5) centimeter per year.\nhow much does the rock formation grow in 50,000 years? write your answer using scientific notation.\n4.5×10² cm\nwhat is a common unit for expressing the height of an object this size?\nmeters\nwrite the amount the rock formation grows in meters. enter your answer in standard form.\n m

a rock formation in a cave grows at a rate of 9×10^(-5) centimeter per year.\nhow much does the rock formation grow in 50,000 years? write your answer using scientific notation.\n4.5×10² cm\nwhat is a common unit for expressing the height of an object this size?\nmeters\nwrite the amount the rock formation grows in meters. enter your answer in standard form.\n m

Answer

Explanation:

Step1: Recall growth rate formula

The growth amount = growth - rate×time. The growth - rate is $9\times10^{-5}$ cm/year and the time is 50000 years.

Step2: Calculate growth in centimeters

$9\times10^{-5}\text{ cm/year}\times50000\text{ years}=9\times10^{-5}\times5\times10^{4}\text{ cm}$. Using the rule of exponents $a^{m}\times a^{n}=a^{m + n}$, we have $9\times5\times10^{-5 + 4}=45\times10^{-1}=4.5\text{ cm}$.

Step3: Convert centimeters to meters

Since 1 m = 100 cm or $1\text{ cm}=10^{-2}\text{ m}$, then $4.5\text{ cm}=4.5\times10^{-2}\text{ m}$.

Answer:

$4.5\times10^{-2}$