A student decides she wants to save money to buy a used car, which costs $2600. She comes up with what she thinks is a very modest savings plan. She decides to save 2 cents the first day and double the amount she saves each day thereafter. On the second day she plans to save 4 cents, on the third day, 8 cents, and so on. Determine how long it will take her to save enough money to buy the car ?

17 days

Step-by-step explanation:

as you see, 4=2^2

and 8=2^3

so we have a number sequence:

2+2^2+2^3+...+2^n=260000 (1)

multiply (1) by 2 we have:

2^2+2^4 +...+2^(n+1)=520000 (2)

(2) minus (1) we have:

2^(n+1)-2=260000

2^n*2=260002

2^n=130001

and we have 2^17=131072 >130001

so it will take her at least 17 days to buy the car

no solution

step-by-step explanation:

there is not enough information in the problem to solve.