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

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

false

step-by-step explanation:

false : it can not go to 9 the highest that part can go is 7

here is your proof