select the correct answer.\nan experiment observing the growth of two germ strand populations finds these…

select the correct answer.\nan experiment observing the growth of two germ strand populations finds these patterns.\n - the population of the first germ is represented by the function $a(x) = (1.3)^{x+9}$.\n - the population of the second germ is represented by the function $b(x) = (1.3)^{4x+1}$.\nwhich function best represents function $r$, the ratio of the population of the second germ to the population of the first germ?\n - a. $r(x) = (1.3)^{3x - 8}$\n - b. $r(x) = (2.6)^{4x^2 + 9}$\n - c. $r(x) = (1.3)^{5x + 10}$\n - d. $r(x) = (2.6)^{3x - 8}$

select the correct answer.\nan experiment observing the growth of two germ strand populations finds these patterns.\n - the population of the first germ is represented by the function $a(x) = (1.3)^{x+9}$.\n - the population of the second germ is represented by the function $b(x) = (1.3)^{4x+1}$.\nwhich function best represents function $r$, the ratio of the population of the second germ to the population of the first germ?\n - a. $r(x) = (1.3)^{3x - 8}$\n - b. $r(x) = (2.6)^{4x^2 + 9}$\n - c. $r(x) = (1.3)^{5x + 10}$\n - d. $r(x) = (2.6)^{3x - 8}$

Answer

Explanation:

Step1: Define the ratio function

The ratio ( R(x) ) of the second germ population to the first is ( R(x)=\frac{B(x)}{A(x)} ). Substitute ( B(x) = (1.3)^{4x + 1} ) and ( A(x)=(1.3)^{x + 9} ), so ( R(x)=\frac{(1.3)^{4x + 1}}{(1.3)^{x + 9}} ).

Step2: Apply exponent rule for division

Using the rule ( \frac{a^m}{a^n}=a^{m - n} ) (where ( a = 1.3 ), ( m = 4x + 1 ), ( n = x + 9 )), we subtract the exponents: ( (4x + 1)-(x + 9)=4x + 1 - x - 9 = 3x - 8 ). Thus, ( R(x)=(1.3)^{3x - 8} ).

Answer:

A. ( R(x) = (1.3)^{3x - 8} )