Step 1: Understanding the Concept
Growth in cells can be arithmetic or geometric. The two types differ in how many daughter cells keep dividing.
Step 2: Arithmetic growth
Only one daughter cell keeps dividing, so a constant amount is added in each unit of time.
Length plotted against time is therefore a straight line, i.e. linear.
Step 3: Geometric growth
Both daughter cells keep dividing, so the size multiplies each time.
The curve rises exponentially after an initial lag phase.
Step 4: Compare the options
Only the option stating linear for arithmetic and exponential for geometric growth matches both facts.
Final Answer:
Arithmetic growth gives a linear curve and geometric growth gives an exponential curve.
\[ \boxed{\text{(C) }\text{Arithmetic growth curve is linear while Geometric growth curve is exponential.}} \]