GED Mathematical Reasoning TestAlgebraic Problem Solving with Expressions and EquationsHard
A financial analyst is comparing two investment options. Investment A grows according to the function A(t) = 500(1.04)^t, and Investment B grows according to B(t) = 450(1.05)^t, where 't' is the number of years. Approximately how many years will it take for Investment B to be worth more than Investment A?
- A8 years
- B15 years
- C10 years
- D12 years
Show answer & explanationAnswer & explanation
Correct answer: C. 10 years
To find when Investment B is worth more than Investment A, we set B(t) > A(t) and solve for 't'. This involves solving an exponential inequality, which can be done by taking logarithms of both sides.
Why the other options are wrong
- A. This value is too low; B is still less than A at this point.
- B. This value is too high; B is significantly more than A at this point.
- D. While B is definitely worth more at 12 years, it surpasses A earlier than this.
Solving Exponential Inequalities
A mathematical statement involving an exponential expression and an inequality symbol (>, <, ≥, ≤). Solving it means finding the range of values for the variable that makes the inequality true.
- Often requires taking logarithms of both sides.
- Remember to reverse the inequality sign if multiplying or dividing by a negative number.
- Can be solved graphically by finding intersection points.
Memory trick: Logarithms Level the Exponential Playing Field.