Word problem on exponential growth

Question

A job pays a salary of $22,000 the first year. During the next 10 years, the salary increases by %4 each year. What is the total lifetime salary over the 11-year period?  

Answer 1

Exponential grown is f(x) = ab^x.

This is not exponential growth.

 

This is the sum of a geometric series:

 

22000 + 22000(1.4) + 22000(1.4)(1.4) + ....

 

S_n = a(1 - rⁿ) / (1 - r), where a = starting amount, r = common ratio, n = number of terms

 

S₁₁ = 22000(1 - 1.4¹¹ ) / (1 - 1.4)

S₁₁ = 22000(1 - 40.495) / -0.6

S₁₁ = 22000(-39.495) / 0.6

S₁₁ = -868890 / -0.6

S₁₁ = 1448150