Logistic and Exponential Models

Let the model for this data be y = 2^x. Find the SS_res accurate to 3 significant figures.

Answer explanation

L3=2^x which is the given model. The SSres is obtained from [2nd][0] for Catalogue and [Alpha][LN] to jump to S. Move to sum( . Enter sum((L3-L2)²) to obtain 0.305.

This function models the number N (in millions) of market-sized oysters in Chesapeake Bay over time t in years since 1994: N(t)= 5089 1+22.344e^{-0.274t} What is the carrying capacity of market-sized oysters in Chesapeake Bay? Include an appropriate label!

How many market-sized oysters were there in 1994?

• 5089 million market-sized oysters

• 22.344 million market-sized oysters

• 218 million market-sized oysters

• 282.9 million market-sized oysters

A green energy campaign is trying to convince households in a target area to switch from incandescent to florescent lightbulbs. There are 241,224 households in this target area.

Initially 184 households make the change. Market research indicates that, in the absence of limiting factors, we could increase that number by 20% each month.

Put K, b, and r together into the correct logistic model for this situation!

As reported in the Washington Post on Thursday, April 2, 2020, the number of reported Carona Virus cases in the Washington DC metropolitan area was 4698. On March 5, the first 3 cases were reported. Using an exponential regression, use the above data to estimate the number of cases in the DC metropolitan area on April 6.

• 7945

• 7495

• 9745

• 9475

A colony of termites is growing continuously at a rate of 6.2% monthly. If the colony starts with 500, how many would there be in one year?

(Enter only the value in the blank. Round to the nearest whole number.)

Mathematical Equivalence

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Suppose an automobile that originally costs $14,000 was to INCREASE its value by 20% every year. What exponential equation can we create to model this situation?

• y=14000(.20)^x

• y=14000(.80)^x

• y=14000(1.20)^x

• y=14000(1.80)^x

A chemist has a 100-gram sample of a radioactive material.  He records the amount of radioactive material every week for 6 weeks and obtains the following data: Find the exponential model of the function.

• y = 100(8.7)^x

• y = 100(1.87)^x

• y = 100(.87)^x

• y = 100(.13)^x

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The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the exponential equation?

• y=8(15,000)^x

• y=15,000(0.92)^x

• y=15,000(1.08)^x

• y=15,000(0.08)^x