Question

for her eight birthday, shelleys grandma gave her a full bag of candy. she counted the candy, and figured out a clever plan, if she only eats half of her candy each day, she wont run out. the number of candy, n, after a certain number of days, x, can be modeled by ( n(x)=160cdot(0.5)^{x} ). note: if she starts eating a candy, she finishes it! has this been modeled by a linear or exponential? what does the 160 mean in terms of the problem situation? what does the 0.5 mean in terms of the problem situation? how much is left in a week (7 days)? ( n(10)=0.15625 ). what does this mean in context?

Explanation:

Step1: Sustituir \(x = 7\) en la ecuación \(N(x)=160\cdot(0.5)^{x}\)

$$N(7)=160\cdot(0.5)^{7}$$

Step2: Calcular \((0.5)^{7}\)

$$(0.5)^{7}=\frac{1}{2^{7}}=\frac{1}{128}$$

Step3: Calcular \(160\cdot\frac{1}{128}\)

$$160\cdot\frac{1}{128}=\frac{160}{128}=\frac{5}{4} = 1.25$$

Answer:

\(1.25\)