Question

Anita bought her phone one year ago for $400, and she wants to eventually sell it to help pay for an upgrade. She checked the manufacturer's website and found that her phone is currently valued at $308, and it will continue to depreciate each year.

Write an exponential equation in the form y - a(b)* that can model the value of Anita's phone, y, × years after purchase.
Use whole numbers, decimals, or simplified fractions for the values of a and b.

Answer 1

this is just a quick addition to the good reply above by "varnanaik"

so she bought it for 400 bucks, but hell a year later went down to 308? Let's find the rate of depreciation

`\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill & \$ 308\\ P=\textit{initial amount}\dotfill &\$400\\ r=rate\to r\%\to (r)/(100)\\ t=years\dotfill &1 \end{cases}`

`308 = 400(1 - (r)/(100))^(1) \implies \cfrac{308}{400}=1-\cfrac{r}{100}\implies \cfrac{77}{100}=\cfrac{100-r}{100} \\\\\\ 77=100-r\implies r+77=100\implies r=\stackrel{ \% }{23} \\\\[-0.35em] ~\dotfill\\\\ A=400(1-(23)/(100))^x\implies A=400(1-0.23)^x\implies {\Large \begin{array}{llll} A=400(0.77)^x \end{array}}`

Answer 2

y= 400(0.77)^x

Explanation:

The value decreases by 23% from,400 to 308 in 1 year. so if this continues then the equation would be y=400(0.77)^x.

The 0.77 comes from decaying 23%, meaning 1-0.23 = 0.77