We have been given that last month Maria purchased a new cell phone for $500. The store manager told her that her cell phone would depreciate by 70% every 6 months.

We know that an exponential function is in form $y=a\cdot (1-r)^x$ , where,

y = Final value,

a = Initial value,

r = Decay rate in decimal form,

x = Time in years.

Let us convert $70\%$ into decimal form.

$70\%=\frac{70}{100}=0.70$

Initial value of car is 500, so $a=500$ .

Since value of phone depreciates every months, so value of phone will depreciate twice in a year.

Upon substituting our given values in exponential decay function, we will get:

$V=500(1-0.70)^{2x}$

To find the value of phone after 2 years, we will substitute $x=2$ in our equation.

$V=500(1-0.70)^{2(\cdot 2)}$

$V=500(1-0.70)^{4}$

Therefore, option D is the correct choice.

Let us simplify our equation.

$V=500(0.30)^{4}$

Therefore, option B is correct as well.

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3 years ago