Electric vehicles displaced 3% of automobile gasoline use, per year, at the end of 2019. This is exponential growth, since the growth depends on a percentage of the initial amount. How long will it take to displace half of the automobile gasoline use (at 3%/yr more displacement), using the exponential equation or its simplification?
Hello,
This question appears trivial (and in all likelihood it is), however It's been quite a while since I've had any sort of math education and so this question is tripping me up. I've tried plugging the 0.03 (3%) into the exponential equation y=a(1+0.03)^x, but this has yielded an answer that is unrealistically low. All other variants of the exponential equation I've tried have yielded either absurdly high or low time estimates, by orders of magnitude. Any insights into this quite simple question will be greatly appreciated.
If we calculate with an actual $3$ percent per year increase (instead of percentage points), the model that we can use to calculate the figure on year $x$ is simply $$ 0.03 \cdot (1.03)^x $$ According to this model, one should wait over $95$ years in order for this to increase above $0.5$.