1. **Stating the problem:** We are given the function $b(t) = 4.5e^{1.4t}$ which models a context or application, possibly related to growth or decay over time $t$. 2. **Formula and explanation:** The function is an exponential function of the form $b(t) = Ae^{kt}$ where $A$ is the initial value and $k$ is the growth rate. 3. **Understanding the components:** Here, $A = 4.5$ and $k = 1.4$. Since $k > 0$, this represents exponential growth. 4. **Intermediate work:** To find the value of $b(t)$ at any time $t$, substitute $t$ into the formula and calculate: $$b(t) = 4.5e^{1.4t}$$ For example, at $t=0$, $$b(0) = 4.5e^{1.4 \times 0} = 4.5e^0 = 4.5 \times 1 = 4.5$$ 5. **Interpretation:** This means the initial value at time zero is 4.5. As $t$ increases, $b(t)$ grows exponentially. 6. **Summary:** The function $b(t) = 4.5e^{1.4t}$ models exponential growth starting at 4.5 when $t=0$ and increasing rapidly as $t$ increases.