Answer:
<em>Student 2 is incorrect because he didn't use the formula properly</em>
Step-by-step explanation:
The exponential function is often used to model natural growing or decaying processes, where the change is proportional to the actual quantity.
An exponential decaying function is expressed as:
![C(t)=C_o\cdot(1-r)^t](https://tex.z-dn.net/?f=C%28t%29%3DC_o%5Ccdot%281-r%29%5Et)
Where:
C(t) is the actual value of the function at time t
Co is the initial value of C at t=0
r is the decaying rate, expressed in decimal
The initial value of the item is Co=$1000, the rate of decay is r=40%=0.4, and the time is t=3 years.
Substituting into the formula:
![C(3)=\$1000\cdot(1-0.4)^3](https://tex.z-dn.net/?f=C%283%29%3D%5C%241000%5Ccdot%281-0.4%29%5E3)
![C(3)=\$1000\cdot0.6^3](https://tex.z-dn.net/?f=C%283%29%3D%5C%241000%5Ccdot0.6%5E3)
C(3)=$216
Student 2 is incorrect because he didn't use the formula properly
<h2><u>Answer</u><u> </u><u>:</u></h2>
![\bigstar\boxed{\large\bf{\leadsto 6\:floors}}](https://tex.z-dn.net/?f=%5Cbigstar%5Cboxed%7B%5Clarge%5Cbf%7B%5Cleadsto%206%5C%3Afloors%7D%7D)
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![\begin{gathered}\rm{ \underline{ \underline{ \red{Given}}}}\begin{cases}\sf{height\:of\:one\:floor\:of\:dollhouse =12.4\:in} & \\ \\\sf{Height\:of\: dollhouse=75\:in}&\end{cases}\\\\\end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%5Crm%7B%20%5Cunderline%7B%20%5Cunderline%7B%20%5Cred%7BGiven%7D%7D%7D%7D%5Cbegin%7Bcases%7D%5Csf%7Bheight%5C%3Aof%5C%3Aone%5C%3Afloor%5C%3Aof%5C%3Adollhouse%20%3D12.4%5C%3Ain%7D%20%26%20%5C%5C%20%5C%5C%5Csf%7BHeight%5C%3Aof%5C%3A%20dollhouse%3D75%5C%3Ain%7D%26%5Cend%7Bcases%7D%5C%5C%5C%5C%5Cend%7Bgathered%7D%20)
<h2><u>To </u><u>find </u><u>:</u></h2>
- Total number of Floors in dool house
<u>➜</u><u> </u><u>Therefore</u><u> </u><u>,</u><u> </u><u>Total</u><u> </u><u>number</u><u> </u><u>of </u><u>floors</u><u> </u><u>can </u><u>be </u><u>find </u><u>out</u><u> </u><u>by </u><u>dividing</u><u> </u><u>the </u><u>total</u><u> </u><u>height</u><u> </u><u>of </u><u>dollhouse</u><u> </u><u>by </u><u>the </u><u>length</u><u> </u><u>of </u><u>one </u><u>floor</u>
![\bf{=\cancel{ \dfrac{75}{12.5}}}](https://tex.z-dn.net/?f=%5Cbf%7B%3D%5Ccancel%7B%20%5Cdfrac%7B75%7D%7B12.5%7D%7D%7D)
![\bf{= 6}](https://tex.z-dn.net/?f=%5Cbf%7B%3D%206%7D)
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I believe you will need to find what -0.125 of an inch is, subtract that from 16, then divide that into 11.