Question

Question 2:Maggie is a DJ. Every week she buys 6 new albums to add to her collection. She currently owns 15 albums.(a) Find a linear model of the form Pt=P0+dt to describe the number of albums that Maggie has at a given point in time.Pt = (b) How many albums will Maggie have in 6 weeks? albums(c) When will Maggie have 25 albums? Round your answer to the nearest tenth of a week.After weeks

Answer 1

(a) Consider that Maggie currently owns 15 albums, this is a constant. Every week, she acquires 6 new albums. You can write this in the following algebraic form:

$P(t)=15+6t$

where t is the number of weeks.

(b) In order to determine the number of albums after 6 weeks, replace t=6 into the previous expression for P(t):

$P(6)=15+6(6)=15+36=51$

Then, Maggie will have 51 albums.

(c) Replace P(t) = 25 into the expression for P(t) and solve for t,as follow:

$\begin{gathered} 25=15+6t \\ 25-15=6t \\ 10=6t \\ \frac{10}{6}=t \\ t\approx1.7 \end{gathered}$

Hence, in approximately 1.7 weeks Maggie will have 25 albums.