a rock formation in a cave grows at a rate of 9×10⁻³ centimeter per year. how much does the rock formation…

Explanation:

Step1: Identify the growth - rate and time

Growth rate $r = 9\times10^{-3}$ cm/year, time $t=50000$ years.

Step2: Use the formula for growth amount

The amount of growth $A = r\times t$. First, write $50000$ in scientific notation as $5\times 10^{4}$. Then $A=(9\times 10^{-3})\times(5\times 10^{4})$.

Step3: Multiply the numbers and add the exponents

Using the rule of exponents $a^{m}\times a^{n}=a^{m + n}$ and $(a\times10^{m})\times(b\times10^{n})=(a\times b)\times10^{m + n}$, we have $(9\times5)\times10^{-3 + 4}=45\times10^{1}$.

Step4: Rewrite in proper scientific notation

$45\times10^{1}=4.5\times10^{2}$ cm.

Answer:

$4.5\times10^{2}$ cm