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, is modeled by the function H(t) = 5 * (1.2)^t. What is the predicted height of the plant after 3 weeks?
- A8.64 cm
- B10.0 cm
- C7.2 cm
- D6.0 cm
Show answer & explanationAnswer & explanation
Correct answer: A. 8.64 cm
To find the predicted height, substitute t=3 into the given exponential function. Calculate 5 * (1.2)^3 to get the result.
Why the other options are wrong
- B. This would be 5 * 2, not related to the exponential growth.
- C. This would be 5 * (1.2)^2, which is the height after 2 weeks.
- D. This would be 5 * 1.2, which is the height after 1 week.
Evaluating Exponential Functions
Substituting a given value for the independent variable into an exponential function to find the corresponding dependent variable value.
- Exponential functions model growth or decay.
- The independent variable is usually time (t) or quantity (x).
- The base of the exponent determines the rate of change.
Memory trick: Plug in the time, watch the height climb!