GED Mathematical Reasoning TestAlgebraic Problem Solving with Graphs and FunctionsMedium
A scientist is tracking the population of a certain bacteria culture. Initially, there are 200 bacteria. The population triples every hour. Which type of function best represents the growth of this bacteria culture, and why?
- ALinear, because the population increases by a constant amount each hour.
- BLogarithmic, because the growth slows down over time.
- CExponential, because the population multiplies by a constant factor each hour.
- DQuadratic, because the growth rate is not constant.
Show answer & explanationAnswer & explanation
Correct answer: C. Exponential, because the population multiplies by a constant factor each hour.
Exponential functions are characterized by a constant multiplicative factor (tripling, doubling, halving) over equal intervals. Linear functions involve a constant additive change. Quadratic functions have a parabolic shape, and logarithmic functions typically model processes that slow down.
Why the other options are wrong
- A. The population triples, it does not increase by a constant amount; this describes linear growth.
- B. Logarithmic growth typically slows down, but this scenario describes rapid increase by multiplication.
- D. While the growth rate isn't constant, 'triples every hour' specifically indicates exponential, not quadratic, behavior.
Exponential Function
A function where the independent variable appears as an exponent, leading to growth or decay by a constant multiplicative factor.
- Form: y = a * b^x (a is initial value, b is growth/decay factor)
- Characterized by rapid increase or decrease
- Common in population growth, compound interest, radioactive decay
Memory trick: Linear is a line, Quad is a curve, Expo is a boom!