GED Mathematical Reasoning TestAlgebraic Problem Solving with Graphs and FunctionsEasy
A scientist is observing the growth of a bacterial colony. The population, P, in thousands, after t hours, is modeled by the function P(t) = 50 * (1.15)^t. What does the value '1.15' represent in this context?
- AThe initial population of the colony.
- BThe total growth in population after one hour.
- CThe number of hours until the population doubles.
- DThe hourly growth factor of the population.
Show answer & explanationAnswer & explanation
Correct answer: D. The hourly growth factor of the population.
In an exponential growth function P(t) = P₀(1 + r)^t, the term (1 + r) is the growth factor. Here, 1.15 is the base of the exponent, representing the factor by which the population multiplies each hour.
Why the other options are wrong
- A. The initial population is P₀, which is 50 in this equation.
- B. The total growth after one hour would be P(1) - P(0), not 1.15.
- C. The doubling time requires solving for t when P(t) = 2 * P₀.
Exponential Growth Function Components
An exponential growth function, typically y = a * b^x, models quantities that increase at a constant percentage rate. 'a' is the initial amount, and 'b' is the growth factor (1 + rate).
- Form: y = a * b^x or y = a * (1 + r)^x
- 'a' = initial amount (y-intercept)
- 'b' = growth factor (b > 1 for growth)
- 'r' = growth rate (as a decimal)
Memory trick: Base is the Booster, Rate is the Reason!