Exponential Equations in Science II: The Constant e and Limits to Growth

The exponential equation N=N₀e^kt is used by many scientists to measure growth and decay. This equation already has the variable of time (t) built into it. Why is time important?

• a.Because environmental conditions change over time, which affects growth and decay.
• b.Because growth and decay in a system does not happen all at once, it takes place over time.
• c.Because growth and decay are unpredictable, scientists need a way to guess at the amount something has changed.
• d.Because scientists can only study something if they can physically measure the start and end points in time.

In science, the constant variable e is BEST described as

• a.the change that takes place at a specific point in time.
• b.the rate of change over time.
• c.the base rate of change in systems that are continuously changing.
• d.the base rate of change in systems that are static.

The constant variable k is used in exponential equations to

• a.modify e for specific circumstances, like changes in material or environmental conditions.
• b.modify e for changes in the amount being measured.
• c.modify N for specific circumstances, like changes in material or environmental conditions.
• d.modify N for changes in the amount being measured.

Study the graph below. Which statement BEST describes the data being shown?

• a.The graph shows the decay rate of a radioactive isotope.
• b.The graph shows the decline of a population of bacteria at different temperatures.
• c.The graph shows the growth rate of a bacteria population over time.
• d.The graph shows the growth rate of bacteria at different temperatures.

The constant variable k is always a positive number.

• a.true
• b.false

There are many forms of exponential equations that scientists use. When studying a population or radioactive material, why wouldn't a scientist use y = ab^x?

• a.Because it does not include the value N, which gives the amount.
• b.Because it does not include the value e, which gives a base value.
• c.Because it does not take into consideration time or the rate of growth or decay.
• d.Because it does not include the value N₀, which gives the amount at time 0.

The variable constant e refers to the limit of the expression (1+1/n)ⁿ. It is considered a limit because the value of the equation reaches a constant as the values of n get larger and larger.

• a.true
• b.false