cientists are studying the population of a particular type to fish. the table below shows the data gathered over-five month time period. use the data to answer question 5-9 months 0,8 fish,month 1-39, month 2-195, month 3-960, month, month 4-4,738, month 5-23,375 the linear transformation model is log y hat=0.9013.log x +0.6935 and it say use the linear transformation model to predict the number of fish in 12 months.
Yeet Sceet like a motha freakin sheet
To predict the number of fish in 12 months using the linear transformation model, you need to follow these steps:
Step 1: Identify the equation of the linear transformation model.
The equation given is: log y_hat = 0.9013 * log x + 0.6935
Step 2: Substitute the value of x with the number of months (12).
Now, we need to substitute x = 12 into the equation to find the corresponding predicted value of y (the number of fish).
log y_hat = 0.9013 * log(12) + 0.6935
Step 3: Calculate the value of log(12).
Using a calculator or logarithm table, find log(12) ≈ 1.0792.
So the equation becomes:
log y_hat = 0.9013 * 1.0792 + 0.6935
Step 4: Simplify the equation.
Multiply the values and add them:
log y_hat ≈ 0.9727 + 0.6935
log y_hat ≈ 1.6662
Step 5: Convert the equation back to exponential form.
To convert the equation back to exponential form, we need to take the antilog (inverse logarithm) of both sides:
y_hat ≈ 10^(1.6662)
Using a calculator, this simplifies to:
y_hat ≈ 47.471
The predicted number of fish in 12 months is approximately 47.471.