HPC 5. 1 Day 3 Exponential Growth and Decay Nov 2024

Front

What is the initial value in the equation P = 8(2.25)^x?

Back

8

Front

Which function shows an initial amount of $15 and an increase of 35% each year?

Back

y = 15(1 + 0.35)^x

Front

Evaluate the expression y=125(1+.08)^5 and round to the nearest tenth.

Back

183.8

Front

What exponential equation represents a 78 gram sample of Uranium that loses half of its mass each year?

Back

y = 78(0.5)^x

Front

Which equation represents a culture of bacteria that begins with 5000 cells and decreases by 30% each year?

Back

y = 5000(0.7)^x

Front

Define exponential growth.

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to growth that accelerates over time.

Front

Define exponential decay.

Back

Exponential decay occurs when a quantity decreases at a rate proportional to its current value, leading to a rapid decrease initially that slows over time.

Front

What is the formula for exponential growth?

Back

The formula is y = a(1 + r)^t, where a is the initial amount, r is the growth rate, and t is time.

Front

What is the formula for exponential decay?

Back

The formula is y = a(1 - r)^t, where a is the initial amount, r is the decay rate, and t is time.

Front

How do you find the half-life of a substance in exponential decay?

Back

The half-life is the time required for a quantity to reduce to half its initial value, calculated using the formula t_{1/2} = \frac{\text{ln}(0.5)}{\text{ln}(1 - r)}.