Question

Suppose that you have a bowl of 500 m&m candies, and each day you eat 1/4 of the candies you have. Is the number of candies left changing linearly or exponentially? Write an equation to model the number of candies left after n days.

Answer 1

Answer:

$500(.75)^{n}$

Step-by-step explanation:

It is changing exponentially because if you are eating a fraction of the left over m & m's, that is a different amount each time so it can't be linear.

500(1-(1/4))^n

$500(.75)^{n}$

Answer 2

Initial quantity of the candies = 500

If we eat $\frac{1}{4}$ candies each day, number of candies after one day

= 500 - $\frac{1}{4}\times 500$

= 500 - 125

= 375

Number of candies after two days

= 375 - $\frac{1}{4}\times (375)$

= 281.25

Therefore, sequence formed will be.

500, 375, 281.25.......n days

Ratio of 2nd and 1st term = $\frac{375}{500}$ = 0.75

Ratio of 3rd and 2nd term = $\frac{281.75}{375}$ = 0.75

Therefore, there is a common ratio of 0.75 in each successive and previous term.

And the sequence will be a geometric sequence.

Expression for the exponential decay is,

$A=A_0(1-r)^n$

Here, A = Final amount

$A_0=$ Initial amount

r = percentage decrease

n = duration

From the given question,

$A_0=500$

r = $\frac{1}{4}=\frac{25}{100}$

Therefore, equation for the decrease in number of candies will be.

$A=500(1-0.25)^n$

$A=500(0.75)^n$

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