# 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
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 $$\displaystyle={0.9692}^{{t}}\times{720}$$
$$\displaystyle={0.97}^{{t}}\times{720}$$
$$\displaystyle{P}{\left({t}\right)}={0.97}^{{t}}\times{720}$$

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