contestada

A group of students retake the written portion of a driver?s test after several months without reviewing the material. A model used by psychologists describes retention of the material by the function a = 90 - 10 log (t + 2), where a is the average score at the time t (in weeks). Use the model to predict the number weeks when the average score is 75.

Respuesta :

Answer: There are 29 weeks approximately when the average score is 75.

Step-by-step explanation:

Since we have given that

[tex]a=90-10\log (t+2)[/tex]

Here, a is the average score.

and t denotes the number of weeks.

Since we have given that the average score is 75.

so, we put a = 75 in the above equation.

[tex]75=90-10\log (t+2)\\\\75-90=-10\log (t+2)\\\\-15=-10\log (t+2)\\\\\frac{15}{10}=\log (t+2)\\\\1.5=\log (t+2)\\\\\text{Taking 10 to the power on both sides}\\\\10^{1.5}=t+2\\\\31.6=t+2\\\\t=31.6-2\\\\t=29.62\ weeks\\\\t\approx 29\ weeks[/tex]

Hence, there are 29 weeks approximately when the average score is 75.

fichoh

Using the retention model, the predicted number of weeks when the average score will be 75 will be 30 weeks.

Given the Parameters :

  • a = 90 - 10 log(t + 2)

  • Average score, a = 75

a = 90 - 10 log(t + 2)

Substitute the value, a = 75 into the equation :

75 = 90 - 10 log(t + 2)

75 - 90 = - 10 log(t + 2)

-15 = - 10 log(t + 2)

Divide both sides by -10 ;

[tex]\frac{-1.5}{-10} = log(t + 2) [/tex]

1.5 = log(t + 2)

Taking 10 to the power will isolate (t + 2) ;

[tex]10^{1.5} = t + 2 [/tex]

[tex] 31.622776 = t + 2 [/tex]

[tex] t = 31.622776 - 2 [/tex]

[tex] t = 29.62 [/tex]

Therefore, there are about 30 weeks when the average score is 75

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