Answer:
No, Deanna will not reach her goal.
Step-by-step explanation:
Let t represent number of years.
We have been given Deanna Jones opened a video rental store this year with 400 tapes. She plans to buy 150 new tapes each year from now on.
We can see that the number of tapes bought by Deanna forms an arithmetic sequence, where 1st term is 400 and common difference is 150.
[tex]A_n=a+(n-1)d[/tex]
a = First terms,
n = Number of terms,
d = Common difference.
Upon substituting our given values, we will get:
[tex]A_n=400+(n-1)150[/tex]
To find the number of tapes that Deanna will have in 5th year, we will substitute [tex]n=5[/tex] in our formula.
[tex]A_5=400+(5-1)150[/tex]
[tex]A_5=400+(4)150[/tex]
[tex]A_5=400+600[/tex]
[tex]A_5=1000[/tex]
Since Deanna will have 1000 tapes in 5th year which is less than 1300, therefore, she will not reach her goal.
