Question =- 10) Many collectibles have values that fluctuate significantly over time. It has been found that the value of a near-mint condition 1951 Bowman Willie Mays baseball card can be approximated by the function B(x) = -15x2 + 450x + 325 on the interval 0 < x < 24 where x is in years and x = 0 corresponds to the year 1983. When (what year) did the maximum value of this baseball card occur and what was the maximum value of this baseball card? NOTE: Doing this problem by trial and error or guess and check will result in a score of 0 points regardless of whether your answer is correct. 11) Find all values of x for which the slope of the line tangent to f(x) = x3 + 15x2 - 160x is equal to 8. arci 14) The temperature of a 167-degree Fahrenheit covered mug of hot chocolate left in a room whose temperature is 71 degrees Fahrenheit can be modeled by the function C(t) = 71 +96e-0.241 where t is in hours and C(t) is in degrees Fahrenheit. Find C'(0.75) and include the units in your answer. 15) Find the instantaneous rate of change of f(x) = 400 – x2 at x = -12. =V 16) For f(x) = -7x+36x-2, find the slope of the secant line from x = -2 to x = 3. Teti 3) The population of Santa Claus, IN has been found to be able to be approximated by the function P(t) = -425 + 488e0.04t for t > 0 where t is in years and t=0 corresponds to the year 1970. When (in what year) will the population be 7,000? = In(13 - 6x) e2-4x 4) Determine the domain of the function f(x) =
BRH3WC The Asker · Calculus
Transcribed Image Text: =- 10) Many collectibles have values that fluctuate significantly over time. It has been found that the value of a near-mint condition 1951 Bowman Willie Mays baseball card can be approximated by the function B(x) = -15x2 + 450x + 325 on the interval 0 < x < 24 where x is in years and x = 0 corresponds to the year 1983. When (what year) did the maximum value of this baseball card occur and what was the maximum value of this baseball card? NOTE: Doing this problem by trial and error or guess and check will result in a score of 0 points regardless of whether your answer is correct. 11) Find all values of x for which the slope of the line tangent to f(x) = x3 + 15x2 - 160x is equal to 8. arci
14) The temperature of a 167-degree Fahrenheit covered mug of hot chocolate left in a room whose temperature is 71 degrees Fahrenheit can be modeled by the function C(t) = 71 +96e-0.241 where t is in hours and C(t) is in degrees Fahrenheit. Find C'(0.75) and include the units in your answer. 15) Find the instantaneous rate of change of f(x) = 400 – x2 at x = -12. =V 16) For f(x) = -7x+36x-2, find the slope of the secant line from x = -2 to x = 3. Teti
3) The population of Santa Claus, IN has been found to be able to be approximated by the function P(t) = -425 + 488e0.04t for t > 0 where t is in years and t=0 corresponds to the year 1970. When (in what year) will the population be 7,000? = In(13 - 6x) e2-4x 4) Determine the domain of the function f(x) =
More Transcribed Image Text: =- 10) Many collectibles have values that fluctuate significantly over time. It has been found that the value of a near-mint condition 1951 Bowman Willie Mays baseball card can be approximated by the function B(x) = -15x2 + 450x + 325 on the interval 0 < x < 24 where x is in years and x = 0 corresponds to the year 1983. When (what year) did the maximum value of this baseball card occur and what was the maximum value of this baseball card? NOTE: Doing this problem by trial and error or guess and check will result in a score of 0 points regardless of whether your answer is correct. 11) Find all values of x for which the slope of the line tangent to f(x) = x3 + 15x2 - 160x is equal to 8. arci
14) The temperature of a 167-degree Fahrenheit covered mug of hot chocolate left in a room whose temperature is 71 degrees Fahrenheit can be modeled by the function C(t) = 71 +96e-0.241 where t is in hours and C(t) is in degrees Fahrenheit. Find C'(0.75) and include the units in your answer. 15) Find the instantaneous rate of change of f(x) = 400 – x2 at x = -12. =V 16) For f(x) = -7x+36x-2, find the slope of the secant line from x = -2 to x = 3. Teti
3) The population of Santa Claus, IN has been found to be able to be approximated by the function P(t) = -425 + 488e0.04t for t > 0 where t is in years and t=0 corresponds to the year 1970. When (in what year) will the population be 7,000? = In(13 - 6x) e2-4x 4) Determine the domain of the function f(x) =
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(10) B(x)=-15x^(2)+450 x+325Sol:- B^(')(x)=(d)/(dx)[B(x)]{:[B^(')(x)=(d)/(dx)[-15x^(2)+450 x+325]],[B^(')(x)=-30 x+450]:}To get maximum or minimum, B^(')(x)=0{:[-30 x+450=0],[-30 x=-450],[x=(450)/(30)=15],[x=15]:}If x=0 for 1983 and x=1 for 1984So x=15 for 1999:. the year to git maximm is 1rag and Maximun Value is B(15)=370 ... See the full answer