1. The problem is to find the value of $N(3)$ given the formula $N(3) = 1000e^{k(3)}$. 2. This formula represents an exponential function where $N(t) = N_0 e^{kt}$, with $N_0$ as the initial amount, $k$ as the growth rate, and $t$ as time. 3. Here, $N_0 = 1000$, $t = 3$, and the expression is $N(3) = 1000e^{3k}$. 4. To evaluate $N(3)$, you need the value of $k$. Without $k$, the expression remains in terms of $k$. 5. If $k$ is known, substitute it into the expression and calculate $N(3)$ using the exponential function. 6. For example, if $k=0.1$, then: $$N(3) = 1000e^{3 \times 0.1} = 1000e^{0.3}$$ 7. Calculate $e^{0.3}$ approximately as $1.3499$, so: $$N(3) \approx 1000 \times 1.3499 = 1349.9$$ 8. Thus, $N(3)$ depends on the value of $k$ and is calculated by substituting $k$ into the formula and evaluating the exponential.