Exponential Growth Calculator

Exponential Growth Calculator: A Simple and Comprehensive Guide

Ever wondered how things grow fast in daily life, like your savings in a bank or how a virus spreads around? That is exponential growth! Or if it's shrinking, like ice melting, it's decay. An online exponential growth/decay calculator makes it easy to figure this out without math headaches. It's a free tool where you just plug in numbers and get quick results.

The key formula is:

x(t) = x0 × (1 + r)^t

Here, x(t) is the value at time t. x0 is your starting amount at time zero. r is the growth rate (if positive, like 5% is 0.05) or decay rate (if negative, like -3% is -0.03). t is the time in whatever units you pick, like years or days. The calculator handles all this in discrete steps.

How to use exponential growth or decay calculator?

Say you invest $150 at 5% interest per year for 10 years. Enter x0=150, r=0.05, t=10. Boom! It spits out about $244.33. That's growth because money compounds on itself.

For decay, lets suppose a phone battery loses 10% charge every hour. x0=100%, r=-0.10, t=5 hours. Result: around 59.05% left. See the curve? It starts slow but speeds up (or down) over time.

This tool is great for students, investors, or anyone planning ahead. Online versions often show graphs too, so you visualize the change. Just remember, r must be decimal, not percent, and pick consistent time units. Real life isn't always perfect—limits like market crashes can hit—but this calculator for exponential growth gives a solid start.