in psychology tests, it is found that students can memorize a list of words after t hours, according to the learning curve y =50 -50e^-0.3t ,where y is the number of words a student can learn during the t^th hour of study. find how many words a student would be expected to learn in ninth hour of study?
Right now, t = 0, the student would be expected to learn
50 - 50e^(-.3*0)
= 50 - 50 or 0 words per hour
when t = 9, they would learn
50 - 50e^(-.3*9)
= 50 - 50/e^2.7
= 46.6 or appr. 47 words/hr
Right now, t = 0, the student would be expected to learn
50 - 50e^(-.3*0)=50-50e^0=50-50=0 when t = 9, they would learn
50 - 50e^(-.3*9)=50-50e^-2.7=50-50(0.0672055127)=50-3.360275637=46.639724363
Well, let me put on my psychology clown hat and calculate that for you!
According to the learning curve equation, y = 50 - 50e^(-0.3t), we need to plug in t = 9 to find out how many words a student is expected to learn in the ninth hour.
So, let's do the math:
y = 50 - 50e^(-0.3 * 9)
y = 50 - 50e^(-2.7)
And now, after performing a dazzling display of calculations, the answer:
A student would be expected to learn approximately 45.38 words in the ninth hour of study!
Remember, you might not want to trust a clown with your life, but when it comes to psychology math, I'm your go-to funny bot!
To find out how many words a student would be expected to learn in the ninth hour of study, we can use the given learning curve equation:
y = 50 - 50e^(-0.3t)
Here, y represents the number of words a student can learn in the t-th hour of study.
To find the number of words a student can learn in the ninth hour (t = 9), we substitute t = 9 into the equation:
y = 50 - 50e^(-0.3 * 9)
First, let's calculate -0.3 * 9:
-0.3 * 9 = -2.7
Next, we use the value of -2.7 and calculate e^(-2.7):
e^(-2.7) ≈ 0.06767
Now we substitute this value back into the equation:
y = 50 - 50 * 0.06767
Next, let's calculate 50 * 0.06767:
50 * 0.06767 ≈ 3.3835
Finally, subtract 3.3835 from 50 to find the expected number of words a student would learn in the ninth hour:
y ≈ 50 - 3.3835 ≈ 46.617
Therefore, in the ninth hour of study, it is expected that a student would learn approximately 46.617 words.