GED Mathematical Reasoning TestAlgebraic Problem Solving with Expressions and EquationsHard
A scientist is tracking the population of a rare species of bird. The population (P) after 't' years can be modeled by the function P(t) = 1500 * (1.05)^t. What will be the approximate population of the birds after 10 years?
- A1575
- B2443
- C1900
- D3000
Show answer & explanationAnswer & explanation
Correct answer: B. 2443
Substitute t=10 into the function: P(10) = 1500 * (1.05)^10. Calculate (1.05)^10 ≈ 1.62889. Then, P(10) = 1500 * 1.62889 ≈ 2443.335, which rounds to 2443.
Why the other options are wrong
- A. This is P(1) = 1500 * 1.05.
- C. Incorrect calculation.
- D. Incorrect calculation; this would be a doubling of the initial population.
Evaluating Exponential Functions (Growth)
Calculating the value of an exponential function at a specific point, often used in scenarios like population growth or compound interest.
- Identify the initial amount, growth rate (or base), and time.
- Substitute the given values for variables into the function.
- Perform the exponentiation first, then multiplication.
Memory trick: Plug in time, watch it climb!