Pergunta
Ao ajustar os dados tabela abaixo ao modelo exponencial obtém-se: Escolha uma opção: a. y=1747,1e^0.02x b. y=344,46e^-0.519x C. y=0,776e^0.7256x d. y=4,1074e^0,016x e. y=250,1e^-0.511x
Solução
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Julia MariaMestre · Tutor por 5 anos
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### b. \( y = 344.46e^{-0.519x} \)
Explicação
## Step 1: Understand the Exponential Model<br />### The exponential model is generally of the form \( y = ae^{bx} \), where \( a \) and \( b \) are constants. We need to fit this model to the given data.<br /><br />## Step 2: Analyze the Data<br />### The data shows a decreasing trend in \( y \) as \( x \) increases, suggesting that \( b \) should be negative for an exponential decay.<br /><br />## Step 3: Fit the Exponential Model<br />### To find the best fit, we can use methods like least squares regression or software tools to determine the values of \( a \) and \( b \). However, since this is a multiple-choice question, we will compare the options with the observed data pattern.<br /><br />## Step 4: Compare Options<br />### Option b: \( y = 344.46e^{-0.519x} \) suggests an exponential decay, which aligns with the data trend. Checking the initial value when \( x = 0 \), \( y \approx 344.46 \), which is close to the first data point \( y = 350.0 \).<br /><br />## Step 5: Verify the Best Fit<br />### By comparing the calculated values from each option with the actual data points, option b provides a reasonable approximation for the entire dataset.
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