There is a local retailer of flavored peanut butters $($Katherine$$s Peanut Butter$).$ The retailer spends $$100/$ month on their social media advertising. The advertisement reaches $10,000$ prospects and from this the retailer gets $120$ new customers a month through these advertisements. So if there are $10,000$ prospects and you get $120$ new customers the current acquisition rate is $120/10,000=0\mathrm{.}012$ or $1\mathrm{.}2\%.$ Your current acquisition rate is $0\mathrm{.}012$ or $1\mathrm{.}2\%.$

You are currently paying $$0\mathrm{.}83$ per new customer. By your estimates, the ceiling rate on any kind of social media advertising $($influencer or traditional$)$ is $10\%.$

Now you are approached by a micro$-$influencer. The influencer has a fairly large social media following $(50$k followers$).$ The micro$-$influencer tells you that she can double the number of customers you acquire if you are willing to pay $$1\mathrm{.}50$ per customer. You$$re thinking, and Katherine $($of Katherine$$s Peanut Butter$)$ is thinking, that$$s CRAZY. I can double the number of customers I acquire by spending only $$0\mathrm{.}67$ more $($$$1\mathrm{.}50-$ $$0\mathrm{.}83).$ Is she true? Calculate the new acquisition rate. Compare the differences. $($Show all your work$)$