Educational psychologists suggest that a child's intellectual capacity, $I$, can be represented as a function of time, $t$, in months, as follows:
$I=f(t)=a\left(1-e^{-b t}\right)$
Where $a0, b0$ are constants. What is the effect on the graph of $I$ of increasing the value of $a$ ?
A) The graph gets closer to the asymptote less quickly.
B) The asymptote moves to the right.
C) The graph gets closer to the asymptote more quickly.
D) The asymptote moves up.

Question

Educational psychologists suggest that a child's intellectual capacity, $I$, can be represented as a function of time, $t$, in months, as follows:
$I=f(t)=a\left(1-e^{-b t}\right)$
Where $a>0, b>0$ are constants. What is the effect on the graph of $I$ of increasing the value of $a$ ?
A) The graph gets closer to the asymptote less quickly.
B) The asymptote moves to the right.
C) The graph gets closer to the asymptote more quickly.
D) The asymptote moves up.

Quizplus · Accepted Answer

Increasing the value of $a$ raises the horizontal asymptote of the function $I=f(t)=a(1-e^{-bt})$ from $I=a$ to a higher value, moving it up.

Educational Psychologists Suggest That a Child's Intellectual Capacity III , Can Be Represented as a Function of Time

Educational Psychologists Suggest That a Child's Intellectual Capacity $I$ , Can Be Represented as a Function of Time