Use the given information to write an exponential equation for y. Does the function represent exponential growth or exponential decay? $\frac { d y } { d t } = 2 y , y = 10 \text { when } t = 0$
A) $y = 10 e ^ { 2 t } , \text {expontial decay }$
B) $y = 10 e ^ { 2 t } , \text {expontial growth }$
C) $y = 10 e ^ { t } , \text { expontial decay }$
D) $y = e ^ { 2 t } , \text { expontial growth }$

Question

Use the given information to write an exponential equation for y. Does the function represent exponential growth or exponential decay? $\frac { d y } { d t } = 2 y , y = 10 \text { when } t = 0$
A) $y = 10 e ^ { 2 t } ,  \text {expontial decay }$
B) $y = 10 e ^ { 2 t } ,  \text {expontial growth }$
C) $y = 10 e ^ { t } , \text { expontial decay }$
D) $y = e ^ { 2 t } , \text { expontial growth }$

Quizplus · Accepted Answer

The given differential equation $\frac { d y } { d t } = 2 y$ suggests an exponential function where the rate of change of $y$ is proportional to its current value. The solution to this differential equation is $y = y_0 e^{kt}$, where $y_0$ is the initial value of $y$ when $t = 0$, and $k$ is the rate of change. Given $y = 10$ when $t = 0$, the initial value $y_0 = 10$, and $k = 2$ from the differential equation, the solution is $y = 10e^{2t}$. Since $k > 0$, this represents exponential growth.

Use the Given Information to Write an Exponential Equation for Y