Question

Ben shared his post with 2 friends. Each of those friends shares with 3 more every day, so the number of shares triples every day.Day
Number of Shares
0 2
1 6
2 18

Write an exponential function to represent the spread of Ben's social media post.

Answer 1

Answer: $y=2(3)^x$

Explanation:

The general exponential function is written as :-

$y=Ab^x--------------(i)$

,where y is the amount of the material after t years , A is the initial amount and b is the multiplicative rate of growth.

From the given table, the number of shares on day 0 = 2 .

Thus the initial number of shares = 2

The growth factor is given by the ratio of the consecutive terms :-

$b=\dfrac{6}{2}=3$

Now, put A = 2 and b = 3 in (i), we get

$y=2(3)^x$

∴ The exponential function to represent the spread of Ben's social media post is $y=2(3)^x$

Answer 2

From the data given above, we can make the following:
N(0) = 2 x 3^0 = 2
N(1) = 2 x 3^1 = 6
N(2) = 2 x 3^2 = 18

An exponential function is represented by:

y = ab^x

where a is the initial value and b is the growth rate.

The exponential function for this case would be:

y = 2(3)^x
y = 6^x