Answer :
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