1. **Problem statement:** Find the intersection point of the function $f(x) = 3 \cdot 1.47^x$ with the y-axis without using a calculator. 2. **Recall the rule for y-axis intersections:** The y-axis corresponds to $x=0$. To find the intersection point, substitute $x=0$ into the function. 3. **Calculate $f(0)$:** $$f(0) = 3 \cdot 1.47^0$$ 4. **Use the exponent rule:** Any number raised to the power 0 equals 1, so $$1.47^0 = 1$$ 5. **Simplify:** $$f(0) = 3 \cdot 1 = 3$$ 6. **Conclusion:** The intersection point with the y-axis is at $(0, 3)$. This can be done without a calculator because raising any nonzero number to the zero power is always 1, so you only multiply 3 by 1.