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Exponential growth and decay

Tell whether the function represents exponential growth or exponential decay. Identify the growth or decay factor. $$\displaystyle{y}={0.15}{\left(\frac{{3}}{{2}}\right)}^{{x}}$$

Exponential growth and decay

Identify each of the following functions as exponential growth or decay. Then give the rate of growth or decay as a percent. $$\displaystyle{y}={a}{\left(\frac{{5}}{{4}}\right)}^{{t}}$$

Exponential growth and decay

What is the Exponential Growth?

Exponential growth and decay

Create an example of sequence of numbers with an exponential growth pattern, and explain how you know that the growth is exponential.

Exponential growth and decay

How can you tell whether an exponential model describes exponential growth or exponential decay?

Exponential growth and decay

The population of a rural community was 3050 in 2010 and the population had increased to 3500 in 2015. Assuming exponential growth find the following. a. The growth rate to 4 decimal places and as a percentage. b. Estimate the population in 2018 if the trend continues.

Exponential growth and decay

If k > 0, the equation $$\displaystyle{y}={y}{0}{e}^{{k}}{t}$$ is a model for exponential (growth/decay), whereas if k >0, the equation is a model for exponential (growth,/decay).

Exponential growth and decay

Diego consumes an energy drink that contains caffeine. After consuming the energy drink, the amount of caffeine in Diego's body decreases exponentially. The 10-hour decay factor for the number of mg of caffeine in Diego's body is 0.2785. 1.What is the 5-hour growth/decay factor for the number of mg of caffeine in Diego's body? 2.What is the 1-hour growth/decay factor for the number of mg of caffeine in Diego's body? 3.If there were 180 mg of caffeine in Diego's body 1.49 hours after consuming the energy drink, how many mg of caffeine is in Diego's body 2.49 hours after consuming the energy drink?

Exponential growth and decay

Determine whether the function represents exponential growth or exponential decay. Then identify the percent rate of change. y=10(1.07)^t

Exponential growth and decay

Consider the following case of exponential growth. Complete parts a through c below. The population of a town with an initial population of 75,000 grows at a rate of 5.5​% per year. a. Create an exponential function of the form $$Q=Q0 xx (1+r)t$$​, ​(where r>0 for growth and r<0 for​ decay) to model the situation described

Exponential growth and decay

Explain the mathematical model for the exponential growth or decay.

Exponential growth and decay

State whether the equation represents exponential growth, exponential decay, or neither. $$\displaystyle{f{{\left({x}\right)}}}={18}{x}^{{2}}$$

Exponential growth and decay

Write an exponential growth or decay function to model each situation. initial value: 50, growth factor: 1.15

Exponential growth and decay

Suppose that  f  is an exponential function with a percentage growth rate of  2% , and with f(0)=147. Find a formula for  f . a) f(t)=0.02t+147 b) f(t)=1.02(1.47)t c) f(t)=147(1.02)t d) f(t)=147(2)t e) f(t)=147(1.20)t

Exponential growth and decay

Describe a difference between exponential growth and logistic growth.

Exponential growth and decay

Tell whether the function represents exponential growth or exponential decay. Explain. $$\displaystyle{y}={3}{\left({0.85}\right)}^{{x}}$$

Exponential growth and decay

The number of teams y remaining in a single elimination tournament can be found using the exponential function $$\displaystyle{y}={128}{\left({\frac{{{1}}}{{{2}}}}\right)}^{{x}}$$ , where x is the number of rounds played in the tournament. a. Determine whether the function represents exponential growth or decay. Explain. b. What does 128 represent in the function? c. What percent of the teams are eliminated after each round? Explain how you know. d. Graph the function. What is a reasonable domain and range for the function? Explain.

Exponential growth and decay

Determine whether the function represents exponential growth or exponential decay. Identify the percent rate of change. f(t)=4(1.05)^t

Exponential growth and decay