Question

Length of the stem at time 0 is 20 cm. The arithmetic growth rate is 30 cm per day. What is the length of the stem at the end of the 7th day?

• A. 460 cm
• B. 50 cm
• C. 170 cm
• D. 230 cm

Hint:

Arithmetic growth means constant increase per unit time. Always use formula \(L_t=L_0+rt\) where growth rate remains fixed.

Answer 1

The Correct Option is D

Concept: Arithmetic growth refers to a pattern of growth in which increase occurs by a constant amount during equal intervals of time. In biological growth patterns, arithmetic growth means the organism increases by a fixed quantity each day rather than increasing proportionally. The mathematical relation used for arithmetic growth is \[ L_t=L_0+rt \] where \[ L_t=\text{Length after time }t \] \[ L_0=\text{Initial length} \] \[ r=\text{Growth rate} \] \[ t=\text{Time} \] Since the increase is constant every day, we directly substitute values into the formula.

Step 1: Identify all quantities given in the question.
The problem states: Initial stem length at time zero \[ L_0=20\;cm \] Arithmetic growth rate \[ r=30\;cm/day \] Time duration \[ t=7\;days \] We now substitute these values into the arithmetic growth formula.

Step 2: Apply arithmetic growth formula.
The formula is \[ L_t=L_0+rt \] Substituting values \[ L_t=20+(30\times7) \] Multiplication gives \[ L_t=20+210 \]

Step 3: Calculate final length.
Adding the two terms \[ L_t=230\;cm \] This means after seven days, the stem length becomes 230 centimeters.

Step 4: Match with answer options.
Checking options: 460 cm → incorrect 50 cm → incorrect 170 cm → incorrect 230 cm → correct Therefore correct answer is \[ \boxed{230\;cm} \] Hence \[ \boxed{\text{Option (4)}} \]