c. \\(\\frac{9^{14}}{9^7}\\)\\n2 a certain type of bacteria reproduces so that after x hours there are…

c. \\(\\frac{9^{14}}{9^7}\\)\\n2 a certain type of bacteria reproduces so that after x hours there are \\(15^x\\) cells. what single power represents the size relationship between the cell population after 24 hours and the cell population after 8 hours? show your work.

c. \\(\\frac{9^{14}}{9^7}\\)\\n2 a certain type of bacteria reproduces so that after x hours there are \\(15^x\\) cells. what single power represents the size relationship between the cell population after 24 hours and the cell population after 8 hours? show your work.

Answer

Explanation:

Step1: Find population at 24 and 8 hours

Population at ( x = 24 ) hours: ( 15^{24} ) Population at ( x = 8 ) hours: ( 15^{8} )

Step2: Find the ratio (relationship)

To find the relationship, divide the population at 24 hours by the population at 8 hours: ( \frac{15^{24}}{15^{8}} ) Using the exponent rule ( \frac{a^m}{a^n}=a^{m - n} ), where ( a = 15 ), ( m = 24 ), ( n = 8 ) ( 15^{24-8}=15^{16} )

Answer:

( 15^{16} )