On what day does the exponential function surpass the quadratic model?

Question

You’ve been offered jobs at two different companies, and each company offers a different form of payment. At one company, each day’s take-home pay will be the sum of that day’s wages plus the previous day’s wages, starting with $1 on the first day and continuing as shown in the table below. The other company will pay you $0.01 on the first day, then double that amount every subsequent day, and is modeled by the equation y = 0.01(2)(x – 1). On what day does the exponential function surpass the quadratic model?

Answer 1

S_first = (x/2)(2 + x - 1)

S_fist = (x/2)(1 + x)

 

S_second = 0.01(1 - 2^x) / (1 - 2)

S_second = -0.01(1 - 2^x)

S_second = 0.01(2^x)

 

(x/2)(1 + x) < 0.01(2^x)

 

Can you solve for x and answser?