Digital SATMath: Advanced MathEasy
A botanist is studying the growth of a rare plant. The height of the plant, H(t), in centimeters, after t weeks can be modeled by the function H(t) = 5(1.2)^t. What is the predicted height of the plant after 3 weeks?
- A9.36 cm
- B8.64 cm
- C10.8 cm
- D6.0 cm
Show answer & explanationAnswer & explanation
Correct answer: B. 8.64 cm
To find the predicted height, substitute t=3 into the given exponential function and calculate the result. H(3) = 5 * (1.2)^3 = 5 * 1.728 = 8.64.
Why the other options are wrong
- A. This might result from a calculation error such as 5 * (1.2 * 3) + 1.2.
- C. This would be 5 * (1.2 * 3), incorrectly multiplying the base by the exponent.
- D. This would be 5 * 1.2, or the height after 1 week.
Evaluating Exponential Functions
Substituting a specific value for the independent variable into an exponential function to find the corresponding dependent variable value.
- Involves a base raised to a power.
- Used to model growth or decay over time.
- Direct substitution is the primary method.
Memory trick: Exponent's path, value in its grasp.