Linear and Exponential Growth

Linear models - change of rate is constant

• y = mx + b; m is the slope / rate of growth (+ for growth, - for decay), b is the starting point

• ex; a library has 8,000 books and is adding 500 more books each year

  • 500x + 8,000

    

    
    

Exponential models - rate of doubling is constant

• f(x) = a^x · b ; a is the base / multiplier (b>1 for growth, b<1 for decay), b is the rate of doubling / starting point

• ex; a bank account starts with $10, every month, the amount gets tripled

  • 3^x · 10