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Answered question

2022-04-15

Find the exponential model that fits the points shown in the table. (Round the exponent to four decimal places.)

x	0	5
y	3	1

Answer & Explanation

nick1337

Expert2022-06-30Added 777 answers

$y = a e^{b x}$

$x = 0, y = 3$

$\Rightarrow 3 = a e^{b (0)}$

$\Rightarrow 3 = a e^{0}$

$\Rightarrow 3 = a$

so, $y = 3 e^{b x}$

now, plug $x - 5, y = 1$

$\Rightarrow 1 = 3 e^{b (5)}$

$\Rightarrow \frac{1}{3} = e^{5 b}$

$\Rightarrow \ln (\frac{1}{3}) = \ln (e^{5 b})$

$\Rightarrow \ln (\frac{1}{3}) = 5 b \ln e$

$\Rightarrow b = \frac{1}{5} \ln (\frac{1}{3})$

$b = - 0.2197$

so, $y = 3 e^{- 0.2197 x}$

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