Digital SATMath: AlgebraMedium
A botanist is studying the growth of a plant. The height of the plant, H, in centimeters, after t weeks is modeled by the function H(t) = 3(1.2)^t. What is the predicted height of the plant after 4 weeks?
- A5.184 cm
- B6.2208 cm
- C7.46496 cm
- D3.6 cm
Show answer & explanationAnswer & explanation
Correct answer: B. 6.2208 cm
To find the height after 4 weeks, substitute t = 4 into the function H(t) = 3(1.2)^t. This yields H(4) = 3 * (1.2)^4. Calculate (1.2)^4 = 2.0736. Then multiply by 3: H(4) = 3 * 2.0736 = 6.2208.
Why the other options are wrong
- A. This is 3 * (1.2)^3, which is the height after 3 weeks. Incorrect exponent.
- C. This is 3 * (1.2)^5, which is the height after 5 weeks. Incorrect exponent.
- D. This is 3 * 1.2, which is the height after 1 week, not 4 weeks. Incorrect exponent application.
Evaluating Exponential Functions
An exponential function is a mathematical function of the form f(x) = a * b^x, where 'a' is the initial value, 'b' is the growth/decay factor, and 'x' is the exponent. Evaluating means finding the output for a given input.
- The variable is in the exponent.
- The base 'b' must be positive and not equal to 1.
- Often models growth or decay over time.
Memory trick: Input goes in, output comes out, like a well-oiled machine.