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Question

Question
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?

Responses
A
1 comma 000 is equal to 24 times 0 point 9 0 5 to the x th power
B
1 comma 000 is equal to 12 times 1 point 0 9 5 to the x th power
C
1 comma 000 is equal to 24 times 1 point 9 5 to the x th power
D

Answer 1

To find the correct equation for the growth of the number of members on the platform, we can use the formula for exponential growth:

\[ N = N_0 \times (1 + r)^x \]

Where:

• \( N \) is the future number of members (1,000 in this case)
• \( N_0 \) is the initial number of members (24 friends)
• \( r \) is the growth rate (9.5% expressed as a decimal is 0.095, so \( 1 + r = 1.095 \))
• \( x \) is the number of weeks

Substituting the values into the formula:

\[ 1000 = 24 \times (1.095)^x \]

From the given choices, we can see that the correct equation is:

B: \( 1,000 = 24 \times 1.095^x \)

So the correct response is B.