HELIXPrep › Engineering Mathematics › Change
Section 1 · Module 1.1 · Topic 1
| Time | Cells |
|---|---|
| 1:00 PM | 1,000 |
| 2:00 PM | 1,200 |
| 3:00 PM | 1,400 |
| 4:00 PM | 1,600 |
| 5:00 PM | 1,800 |
| 6:00 PM | 2,000 |
| 7:00 PM | 2,200 |
How fast are the bacteria growing?
Zooming in — 1:00 PM → 2:00 PM
| Time | Cells |
|---|---|
| 1:00 PM | 1,000 |
| ↳1:18 PM | 1,000 |
| ↳1:30 PM | 1,050 |
| ↳1:52 PM | 1,190 |
| 2:00 PM | 1,200 |
Were the cells growing equally fast during the entire hour?
At exactly 1:37 PM, how fast were the cells growing?
If a car travels
60 km in 1 hour
did it move at exactly
60 km/h the whole time?
The answer is NO
So, Average speed ≠ Current speed
Growth rate behaves exactly like speed.
Average growth rate
is not necessarily
current growth rate.
Now you see it
The dashed secant line between A and B gives the average rate. Drag A and B closer together. Watch what happens to the line — and the number.
Drag A and B closer together →
Memory Cards
Tap each card to reveal the answer.
Where will this idea reappear?
We now know average change.
But how can we calculate
change at a single instant?
Mathematically,
an instant has zero duration.
So how can anything be measured there?
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