A heat probe is attached to the heat exchanger of a heating system. The temperature T (in degrees Celsius) is recorded t seconds after the furnace is started. A model for the data recorded
For the first two minutes is given by $T = \frac { 1351 + 78 t } { 54 + t } . \text { Find } \lim _ { t \rightarrow \infty } T$
A) $1429 ^ { \circ }$
B) $1351 ^ { \circ }$
C) $54 ^ { \circ }$
D) $78 ^ { \circ }$
E) $25 ^ { \circ }$

Question

A heat probe is attached to the heat exchanger of a heating system. The temperature T (in degrees Celsius) is recorded t seconds after the furnace is started. A model for the data recorded
For the first two minutes is given by $T = \frac { 1351 + 78 t } { 54 + t } . \text { Find } \lim _ { t \rightarrow \infty } T$ 
A) $1429 ^ { \circ }$
B) $1351 ^ { \circ }$
C) $54 ^ { \circ }$
D) $78 ^ { \circ }$
E) $25 ^ { \circ }$

Quizplus · Accepted Answer

To find $\lim _ { t \rightarrow \infty } T$, we simplify the expression by dividing the numerator and the denominator by $t$, the highest power of $t$ in the denominator. This gives us $\lim _ { t \rightarrow \infty } \frac { 1351/t + 78 } { 54/t + 1 }$. As $t$ approaches infinity, $1351/t$ and $54/t$ approach 0, leaving us with $\lim _ { t \rightarrow \infty } \frac { 78 } { 1 } = 78$.

A Heat Probe Is Attached to the Heat Exchanger of a Heating