GED Mathematical Reasoning TestAlgebraic Problem Solving with Graphs and FunctionsMedium
A financial analyst is comparing two investment options. Investment A grows according to the function A(t) = 100(1.05)^t, and Investment B grows according to B(t) = 100 + 10t, where t is the number of years. Which statement accurately describes the growth of these investments?
- ABoth investments grow linearly.
- BInvestment A grows linearly, and Investment B grows exponentially.
- CBoth investments grow exponentially.
- DInvestment A grows exponentially, and Investment B grows linearly.
Show answer & explanationAnswer & explanation
Correct answer: D. Investment A grows exponentially, and Investment B grows linearly.
Investment A, A(t) = 100(1.05)^t, is in the form y = ab^x, which is an exponential function because the variable 't' is in the exponent. Investment B, B(t) = 100 + 10t, is in the form y = mx + b, which is a linear function because 't' is raised to the power of 1.
Why the other options are wrong
- A. Incorrect. A is exponential.
- B. Incorrect. A is exponential, B is linear.
- C. Incorrect. B is linear.
Linear vs. Exponential Functions
Linear functions have a constant rate of change (slope) and are of the form y = mx + b. Exponential functions have a constant multiplication factor (growth/decay rate) and are of the form y = ab^x, where the variable is in the exponent.
- Linear graphs are straight lines; exponential graphs are curves.
- Linear change involves adding/subtracting the same amount; exponential change involves multiplying/dividing by the same factor.
- The independent variable in an exponential function is an exponent.
Memory trick: Linear is a line, Exponential is an exponent!