GED Mathematical Reasoning TestAlgebraic Problem Solving with Graphs and FunctionsMedium
A scientist is observing the growth of a bacterial colony. The population, P, in thousands, can be modeled by the function P(t) = 50 * (1.1)^t, where t is the number of hours since the observation began. What does the value '1.1' represent in this function?
- AThe growth factor per hour.
- BThe number of hours passed.
- CThe initial population of the colony.
- DThe percentage increase in population per hour.
Show answer & explanationAnswer & explanation
Correct answer: A. The growth factor per hour.
In an exponential growth function of the form P(t) = a * b^t, 'a' represents the initial amount, 'b' represents the growth factor, and 't' represents the time. The growth factor is (1 + growth rate).
Why the other options are wrong
- B. The number of hours passed is represented by 't' (the exponent), not '1.1'.
- C. The initial population is represented by '50' (the 'a' value), not '1.1'.
- D. The percentage increase is 10% (0.1), as the growth factor is 1 + 0.1. The value 1.1 is the growth factor itself, not just the percentage increase.
Exponential Growth Function Components
An exponential growth function is typically written as y = a(b)^x, where 'a' is the initial value, 'b' is the growth factor (1 + growth rate), and 'x' is the time or number of periods.
- 'a' is the y-intercept (when x=0)
- 'b' > 1 for growth, 'b' < 1 for decay
- Growth rate = b - 1 (expressed as a decimal)
Memory trick: A is for initial Amount, B is for the Boost!