two dozen college friends decided to launch a new social media platform with just their group as the initial…

two dozen college friends decided to launch a new social media platform with just their group as the initial set of members on the platform. the number of members for this social media platform increases at a rate of 9.5% each week. which equation can be used to find the number of weeks, (x), after launching that it takes this platform to grow to 1,000 members? a (1,000 = 24(0.905)^{x}) b (1,000 = 12(1.095)^{x}) c (1,000 = 24(1.95)^{x}) d (1,000 = 24(1.095)^{x})

two dozen college friends decided to launch a new social media platform with just their group as the initial set of members on the platform. the number of members for this social media platform increases at a rate of 9.5% each week. which equation can be used to find the number of weeks, (x), after launching that it takes this platform to grow to 1,000 members? a (1,000 = 24(0.905)^{x}) b (1,000 = 12(1.095)^{x}) c (1,000 = 24(1.95)^{x}) d (1,000 = 24(1.095)^{x})

Answer

Answer:

D. $1,000 = 24(1.095)^{x}$

Explanation:

Step1: Determine initial number of members

Two dozen is 24, so initial members $a = 24$.

Step2: Identify growth - rate factor

Growth rate is 9.5% or 0.095. The growth - factor $r=1 + 0.095=1.095$.

Step3: Use compound - growth formula

The general compound - growth formula is $y=a(1 + r)^{x}$, where $y$ is the final amount, $a$ is the initial amount, $r$ is the growth rate, and $x$ is the number of time - periods. Substituting $y = 1000$, $a = 24$, and $r=0.095$ gives $1000 = 24(1.095)^{x}$.