04.05 graphing exponential functions
write an exponential function to represent the spread of ben's social media post.
write an exponential function to represent the spread of carter's social media post.
graph each function using at least 3 points for each line. all graphs should be placed together on the same coordinate plane, so be sure to label each line. you may graph your equation by hand on a piece of paper and scan your work or you may use graphing technology.
using the functions for each student, predict how many shares each student's post will have received on day 3 and then on day 10. justify your answers.
if amber decides to mail copies of her photo to the 45 residents of her grandmother's assisted living facility, the new function representing her photo shares is f(x) = 3(4)x + 45. how does this graph compare with the original graph of amber's photo share?
based on your results, which students' post travels the fastest? how is this shown in the equation form of the functions?
if you had to choose, would you prefer a post with fewer friends initially but more shares, like amber, or more friends initially but fewer shares? justify your answer with your calculations from previous questions.

An exponential function is a function of the form
,
where a is the starting value or the initial value, b is the base or the rate of growth/decay and x is the input variable representing the number of periods elapsed.


1.) to write an exponential function to represent the spread of ben's social media post, we note firstly that the initial number of shares for ben is 2 shares and the number of shares grows at a rate of 3 shares per person.

therefore, the exponential function representing the spread of ben's social media post is given by



2.) to write an exponential function to represent the spread of carter's social media post, we note firstly that the initial number of shares for carter is 10 shares and the number of shares grows at a rate of 2 shares per person.

therefore, the exponential function representing the spread of carter's social media post is given by



3.) the graph of the functions is attached. the green line represents the social media post of amber, the orange line represents the social meda post of ben while the purple line represent the social media post of carter.


4.) using amber's function,
,
for day 3, x = 3. the number of shares amber's post would have received on day 3 is given by

and for day 10, x = 10. the number of shares amber's post would have received on day 10 is given by


using ben's function,
,
for day 3, x = 3. the number of shares ben's post would have received on day 3 is given by

and for day 10, x = 10. the number of shares ben's post would have received on day 10 is given by


using carter's function,
,
for day 3, x = 3. the number of shares carter's post would have received on day 3 is given by

and for day 10, x = 10. the number of shares carter's post would have received on day 10 is given by



5.) the graph of the new function representing amber's photo share against the old function is attached. the black line represents the new function while the green line represents the old function.

the graph of the new function representing amber's photo share after she mailed copies of her photo to the 45 residents of her grandmother's assisted living facility is the same as the graph of the old function, but the graph of the new function is translated (shifted) up by 45 units.


6.) based on our result, amber's post travel fastest.
in an exponential function, the base (growth factor) determines how fast the function grows. the greater the growth factor, the faster the growth of the function.
therefore, since amber's growth factor is 4, which is greater than ben's 3 and carter's 2, ambers post travels fastest.

7.) because, i would want my post to spread faster, i would prefer a post with fewer friends initially but more shares. based on the explanations given in question 6 above. the greater the growth factor (in our case: the number of shares), the faster the spread of the function (the faster the spread of the post).