VVebWOrk 3: Problem 13 (1 point) Find the long run behavior of each of the following functions. If the function goes to $$ \infty $$ or $$ -\infty $$ enter INFINITY or - INFINITY respectively. (a) As $$ x \longrightarrow \infty, 6(0.7)^{x} \longrightarrow \square $$ (b) As $$ t \longrightarrow \infty, 11(2.3)^{t} \longrightarrow \square $$ (c) As $$ t \longrightarrow \infty, 0.6\left(2+(0.8)^{t}\right) \longrightarrow \square $$

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UpStudy AI · Accepted Answer

**(a)**  
We have the function  
$$
6(0.7)^x.
$$  
Since $$0.7 < 1$$, as $$x \to \infty$$,  
$$
(0.7)^x \to 0.
$$  
Thus,  
$$
6(0.7)^x \to 6 \cdot 0 = 0.
$$  
$$\boxed{0}$$

---

**(b)**  
We have the function  
$$
11(2.3)^t.
$$  
Since $$2.3 > 1$$, as $$t \to \infty$$,  
$$
(2.3)^t \to \infty.
$$  
Hence,  
$$
11(2.3)^t \to 11 \cdot \infty = \text{INFINITY}.
$$  
$$\boxed{\text{INFINITY}}$$

---

**(c)**  
We have the function  
$$
0.6\Bigl(2 + (0.8)^t\Bigr).
$$  
For $$0.8 < 1$$, as $$t \to \infty$$,  
$$
(0.8)^t \to 0.
$$  
So, the function becomes  
$$
0.6\Bigl(2 + 0\Bigr) = 0.6 \cdot 2 = 1.2.
$$  
$$\boxed{1.2}$$
**(a)** As $$ x \to \infty $$, $$ 6(0.7)^x \to 0 $$. **(b)** As $$ t \to \infty $$, $$ 11(2.3)^t \to \text{INFINITY} $$. **(c)** As $$ t \to \infty $$, $$ 0.6(2 + (0.8)^t) \to 1.2 $$.

VVebWOrk 3: Problem 13
(1 point)
Find the long run behavior of each of the following functions. If the function goes to or enter INFINITY or - INFINITY respectively.
(a) As
(b) As
© As

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VVebWOrk 3: Problem 13 (1 point) Find the long run behavior of each of the following functions. If the function goes to or enter INFINITY or - INFINITY respectively. (a) As (b) As © As