. The percentage of American households who have a (color) television grew steadily since its first widespread availability in the early 1960s. It is well modeled by this function: p(t) = 97/ 1 + 30e^−0.27t where t = years since 1960. (a)  Sketch a well-labeled graph of this function for the years 1960-2020. What type of function is this? (b)  According to the model function, what percentage of American households did not own a color television in 2020? (c) When, if ever, will this percentage reach 100%?

Q: Starting with the graph of f(x) = 4^x, find a formula for the function that results from: a.…

A: The given function is   f(x) = 4^x a. Shifting 4 units upwards                  f1(x) = 4 + 4^x b.…

Q: Let the function C� represent the drug concentration in mg/ml of a certain drug at the time t� (in…

A:

Q: I cannot visualize this question. Could you please draw a graph and label all the critical points…

A: Given: First water level rose faster and faster, then rose more but slowly until it reaches its…

Q: Below are data on the population of a species of moths that inhabit an island and breed annually…

A: Pn=1+rPn-1+μ n is the year after 2000 Year Moth 2000 6000 2001 7800 2002 9960

Q: How to solve functions on a graph?

A: 1st draw a graph.

Q: 1) A microorganism is observed to double its population every 3 weeks. Supposed that there were 10…

A: As per our guidelines, we can answer only three sub-parts in a single request. Kindly re-post the…

Q: Poverty Threshold Using data from selected yearsfrom 1990 and projected to 2013, the yearly…

A: Consider the given function.  y=-0.200x3 +7.494x2 +159.305x+6685.097 (a) Graph this function on the…

Q: 8. The percent p a stock price has fluctuated in one year can be modeled by p(x) = 0.0005x¹-0.0193x³…

A: The percent p of a stock price has fluctuated in one year can be written as  where x is the number…

Q: A. If f(x)=2^X, show that f(x+1)=2f(x) B. Translating the graph of f 1 unit (left or right?) is…

A: A.     Given that  f(x)=2x Then  f(x+1)=2x+1                                                     ⇒…

Q: The depreciation of a new boat can be described by f (x) = 650,000 · 0.85*. By how many percent does…

A: Given, The depreciation of new boat is described by the function fx=650,000·0.85x Let, The boat…

Q: 9. A function modeling the number of AIDS cases reported t years after 1990 in a certain location is…

A:

Q: 4- What's the problem with seasonality and what function is used to remove this problem?

A: A time series data is a type data that are collected over an interval of time. It is a technique to…

Q: (a) find the value of A and a, correct to 3 decimal places, (b) predict the percentage of…

A: Topic:- exponential function

Q: A certain drug was administered and the function N (t)= 200(0.85)^(t-1)  represents the amount of…

A:

Q: (a) Draw tangent lines for 1982, 1990, 1995, and 2000. Estimate their slopes. Record the slopes.…

A: Draw the tangent lines for the years 1982, 1990, 1995, and 2000 as follows.

Q: The number of air safety inspectors for selected years is shown in the table. Year 1996 1997 1998…

A: a) x y x2 y2 x⋅y 1996 3349 3984016 11215801 6684604 1997 3155 3988009 9954025 6300535 1998…

Q: 2. It has been observed that a mothball of radius 1 cm evaporates to leave a ball of radius 1/2 cm…

A: We will use rate of evaporation ( change in surface area ) is proportional to surface area formed a…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.