Question

ww2: problem 4 (1 point) find the long run behavior of each of the following functions. (a) as (x\toinfty), (2(0.8)^x\to) inf (b) as (t\to-infty), (15(2.2)^t\to) -inf (c) as (t\toinfty), (0.6(3-(0.6)^t)\to) note: type inf for (infty) and -inf for (-infty). if the limit does not exist in another way, write dne. note: you can earn partial credit on this problem. preview my answers submit answers you have attempted this problem 0 times. you have unlimited attempts remaining.

Explanation:

Step1: Analyze part (a)

For the function $y = 2(0.8)^x$, since $0<0.8 < 1$, as $x\to\infty$, the exponential term $(0.8)^x\to0$. So $2(0.8)^x\to0$.

Step2: Analyze part (b)

For the function $y = 15(2.2)^t$, since $2.2>1$, as $t\to-\infty$, the exponential term $(2.2)^t=\frac{1}{(2.2)^{-t}}\to0$. So $15(2.2)^t\to0$.

Step3: Analyze part (c)

For the function $y = 0.6(3-(0.6)^t)$, as $t\to\infty$, since $0 < 0.6<1$, $(0.6)^t\to0$. Then $y=0.6(3 - 0)=1.8$.

Answer:

(a) $0$
(b) $0$
(c) $1.8$