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- Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it continues on its course indefinitely. Let D(t) denote its distance from Earth after t years of travel. Do you expect that D has a limiting value?Find the constant of proportionality. z is directly proportional to the sum of x and y. If x=2 and y=5, then z=28.The number of bacteria in a refrigerated food product is given by N(T)=23T256T+1,3T33 ,where T is the temperature of the food. When the food is removed from the refrigerator, the temperature is given by T(t)=5t+1.5 , where t is the time in hours. a. Find the composite function N(T(t)) . b. Find the time (round to two decimal places) when the bacteria count reaches 6,752.
- Find the constant of proportionality. y is directly proportional to x. If x=30, then y=15.Kim throws a ball against a wall at time t = 0 At time t = 1 , it hits the wall and then at time t = 2 it is back where it started. If the average speed of the ball is 10 miles per hour, can you apply the MVT to show that the baseball must be traveling at 10 miles / h * r at some point between [0, 2]After an antibiotic tablet is taken, the concentration of the antibiotic in the bloodstream ismodeled by the functionC(t) = 8 (e– 0.4t – e – 0.6t)Where the time t is measured in hours and C is measured in μg/mL. When and what is themaximum and minimum concentration of the antibiotic during the first 12 hours?
- Juaquim's starting salary at a company is $42,000 per year. On average, employees receive a 6.5% increase in salary every year. Which equation shows what his salary will be in x years? A) s=(1+0.065)xs=(1+0.065)x A), s is equal to open paren 1 plus 0 point 0 6 5 close paren to the x th power B) s=42000(1+0.065)xs=42000(1+0.065)x B), s is equal to 42000 times open paren 1 plus 0 point 0 6 5 close paren to the x th power C) s=42000(0.065)xs=42000(0.065)x C), s is equal to 42000 times 0 point 0 6 5 to the x th power D) s=42000(1−0.065)xThe number N of bacteria in a refrigerated food is given by N(T)=20T^2-80T +500, 2<T<14 where T is the temperature of the food in degrees Celsius. When the food is removed from refrigeration the temperature of the food is given by T(t)= 4t +2 , 0<t<3 Where t is the time in hours 1) Find and interpret (N*T)(t) 2) Find the time when the bacteria count reaches 2000 N(T)=20T^2-80T +200, 2<T<12 where T is the temperature of the food in degrees Celsius. When the food is removed from refrigeration the temperature of the food is given by T(t)= 4t +2 , 0<t<5 Where t is the time in hours 3) Find and interpret (N*T)(t) 4) Find the time when the bacteria count reaches 1000Determine the linear approximation for 2√x at x = 5. Use the linear approximation to approximate the value of 2√5.12
- a) How many miles did chloe travel from time t=0 to time t=2 b)at time t=3, is chloes speed increasing or decreasing? give a reason for your awnser c)Is there a time t, for 0≤t≤4 at wich brandons acceleration is equal to 2.5 miles per hour? justify your awnser d) is there a time for 0≤t≤2 at wich brandons velocity is equal to chloes velocity? justify your awnserUse differential approximations in the following problem. A company will sell N units of a product after spending $x thousand in advertising, as given by N=60x-x^2, 5<=x<=30. Approximately what increase in sales will result by increasing the advertising budget from $5,000 to $6,000? From $20,000 to $21,000Find the linear approximation L(x) of the function g(x)= ∛(2+x ) at a = 0 and use it to approximate ∛2.2 , ∛0.65