Question

Luis has saved $6. he doubles the amount he saves each week.does this represent an exponential function?complete:

Answer 1

Answer:

This $6(2)^{n-1}$ 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 $6(2)^{n-1}$, where 'n' is a natural number.

Also, 6, 12, 24, 48,.....

The numbers are increasing by the factor = $\frac{12}{6}=\frac{24}{12}=....=2$

Hence, we get,

This $6(2)^{n-1}$ represent an exponential function, because his savings increase by a constant factor of 2.