Answer:
This [tex]6(2)^{n-1}[/tex] represent an exponential function, because his savings increase by a constant factor of 2.
Step-by-step explanation:
It is given that,
Luis has saved $6 and he doubles the amount each week.
So, the amount saved in the next week = 6×2 = 12
This gives the amount saved in the third week = 12×2 = 24
So, we get the sequence 6, 12, 24, 48,.....
It can be written as, 6×2⁰, 6×2¹, 6×2², 6×2³,.....
So, the sequence in the exponential form [tex]6(2)^{n-1}[/tex], where 'n' is a natural number.
Also, 6, 12, 24, 48,.....
The numbers are increasing by the factor = [tex]\frac{12}{6}=\frac{24}{12}=....=2[/tex]
Hence, we get,
This [tex]6(2)^{n-1}[/tex] represent an exponential function, because his savings increase by a constant factor of 2.
