Answered

IDNLearn.com provides a collaborative platform for sharing and gaining knowledge. Our platform offers detailed and accurate responses from experts, helping you navigate any topic with confidence.

Carla wants to buy a new bike before summer starts in one week. She saves $1 on the first day of the week, $2 on the second day, $4 on thethird day, $8 on the fourth day, and continues this pattern the rest of the week.If the bike costs $150, Carla willenough money to buy the bike before the start of summer.Carla will have

Sagot :

Let's begin by listing out the information given to us:

Time to summer (t) = 1 week = 7 days

First day = $1

Second day = $2

Third day = $4

Fourth day = $8

Fifth day = ?

Sixth day = ?

Seventh day = ?

With the passing of each day, Carla saves double the amount of the previous day. Represented by the geometric progression:

[tex]\begin{gathered} f(x)=2^{x-1} \\ f(1)=2^{1-1}=2^0=1 \\ f(2)=2^{2-1}=2^1=2 \\ f(3)=2^{3-1}=2^2=4 \\ f(4)=2^{4-1}=2^3=8 \\ f(5)=2^{5-1}=2^4=16 \\ f(6)=2^{6-1}=2^5=32 \\ f(7)=2^{7-1}=2^6=64 \end{gathered}[/tex]

On the fifth, sixth & seventh day, Carla saved $16, $32 & $64 respectively.

In 1 week (7 days), Carla saved $127

If the bike costs $150, Carla only has $127 of the said sum:

[tex]127-150=-23[/tex]

Therefore, Carla needs $23 more to be able to purchase the bike before summer

Hence, Carla will not have enough money to buy the bike before summer

We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Accurate answers are just a click away at IDNLearn.com. Thanks for stopping by, and come back for more reliable solutions.