Question

Yao is conducting a biology experiment. He uses the function f(t)=22(1.5)t to represent the total number of bacteria over time, t, in days. Explain the meaning of 1.5 in Yao’s experiment.

Answer 1

Answer:

   Use the exponential growth model in applications, including population growth and compound interest.

   Explain the concept of doubling time.

   Use the exponential decay model in applications, including radioactive decay and Newton’s law of cooling.

   Explain the concept of half-life.

Step-by-step explanation:

Answer 2

Answer:

Exponential growth exists as a pattern of data that shows sharper increases over time.

Step-by-step explanation:

Given,

Yao exists conducting a biology experiment. He utilizes the function f(t)=22(1.5)t to describe the total number of bacteria over time, t, in days.

Exponential growth exists as a pattern of data that shows sharper increases over time. In finance, compounding makes exponential returns. Savings accounts with a compounding interest rate can indicate exponential growth.

Here it is provided that

$f(t)=22 \times(1.5)^{t}$

Which can be rewritten as,

$&f(t)=22 \times(1+0.5)^{t}$

$&\Longrightarrow f(t)=22 \times\left(1+\frac{5}{10}\right)^{t}$

$&\Longrightarrow f(t)=22 \times\left(1+\frac{50}{100}\right)^{t}$

The number of bacteria at the initial stage =22

The rate of increase per day =50%

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