Suppose you purchase an iphoneX for $720 when it initially launched. The resale value decreases 3.08% each month since launch. Write an exponential function that models this situation, where t is the number of months after launch. Call it P(t). (round to the nearest thousandth.)

Suppose you purchase an iphoneX for $720 when it initially launched. The resale value decreases 3.08% each month since launch. Write an exponential function that models this situation, where t is the number of months after launch. Call it P(t). (round to the nearest thousandth.)

Question
Exponential models
asked 2020-11-01
Suppose you purchase an iphoneX for $720 when it initially launched. The resale value decreases 3.08% each month since launch. Write an exponential function that models this situation, where t is the number of months after launch. Call it P(t). (round to the nearest thousandth.)

Answers (1)

2020-11-02
Given,
Suppose you purchase an iPhone X for $720 when it initially launched. The resale value decreases 3.08% each month since launch.
So, the price of the iPhone X after 1 month \(\displaystyle={\left({\frac{{{100}-{3.08}}}{{{100}}}}\right)}\times{720}\)
\(\displaystyle={0.9692}\times{720}\)
Again, the price of the iPhone X after 2 months \(\displaystyle={\left({\frac{{{100}-{3.08}}}{{{100}}}}\right)}\times{0.9692}\times{720}\)
\(\displaystyle={0.9692}^{{2}}\times{720}\)
Therefore, the price of the iPhone X after t month \(\displaystyle={0.9692}^{{t}}\times{720}\)
\(\displaystyle={0.97}^{{t}}\times{720}\)
ANSWER
\(\displaystyle{P}{\left({t}\right)}={0.97}^{{t}}\times{720}\)
0

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