Question

In a Psychology class, the students were tested at the end of the course on a final exam. Then they were retested with an equivalent test at subsequent time intervals. Their average scores after t months are given in the table: Time,t (in months)_11 2 3 4 5 Score, y (%) | 86.2 85.7 85.4 85.2 85.0 Using a graphing utility, fit an exponential function to the data. Use the function you found to estimate how long will it take for the test scores to fall below 84%, rounded to the nearest month. y = 86.37 * x. 9966, 10 months y = 99.66 (0.8637)*: 2 months y = 86.37 (0.9966)*: 8 months There is not enough information to determine this

Answer 1

The functions we found estimate will take 8 months for the test scores to fall below 84%, rounded to the nearest month. The correct option is (c) y = 86.37 (0.9966)*: 8 months.

Given :

n = 5

Let y = $A(B)^{x}$

ln y = ln $A(B)^{x}$

ln y = ln A + ln $B^x$

ln y = ln A + $x$ln B

↓         ↓          ↓

y         c          b

y = c + bx

∑$x = 15$

∑$x^{2} = 55$

∑$xy = 66.6936761$

∑$y = 22.2451514$

b = [$n$∑$xy$- ∑$x$∑$y$] / ($n$∑$x^{2}$ - (∑$x$)^2)]

b = [5 x 66.6936761 - 15 x 22.2451514]

               5 x 55 - 15 x 15

b = - 0.00338893

c = (∑$y$ - $b$∑$x$)/n

c = 22.2451514 + 0.00338893

                  5

c = 4.45867116

A = $e^c = 86.3726574$

B = $e^b = 0.996616806$

y = $86.3726574$ (0.996616806)^x

when y≤84%

$86.3726574$ (0.996616806)^x ≤84%

x≥8.219

x≈8 months

Function, y = 86.37(0.9966)^x

t = x = 8 months.

It will take 8 months time to take for the test scores to fall below 84%. The correct option is (c) y = 86.37 (0.9966)*: 8 months.

To learn more about the functions visit: https://brainly.com/question/28303908

#SPJ4