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HISU UNICAR HUN OMAGGIOI TU LARVEST, 3. Elphaba the squirrel, the notorious criminal, is planning a prison escape. To aid her in her escape, her friend Walt has concocted a supplement that will make her stronger and more agile. The concentration 7(t) of the supplement in Elphaba's system, in mg/ml, t minutes after it is administered is given by the formula T(t) where a and b are constants. = Sat³ b(t-6)² + 10 I for 0 ≤t≤5 for 5

HISU UNICAR HUN OMAGGIOI TU LARVEST, 3. Elphaba the squirrel, the notorious criminal, is planning a prison escape. To aid her in her escape, her friend Walt has concocted a supplement that will make her stronger and more agile. The concentration 7(t) of the supplement in Elphaba's system, in mg/ml, t minutes after it is administered is given by the formula T(t) where a and b are constants. = Sat³ b(t-6)² + 10 I for 0 ≤t≤5 for 5

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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I cannot figure out how to find the numerical values of a and b. I’ve gotten a=125/(b+10) and b=125a-10, but I need to find the exact values of a and b.
3. Elphaba the squirrel, the notorious criminal, is planning a prison escape. To aid her in her escape, her friend Walt has concocted a supplement that will make her stronger and more agile. The concentration 7(t) of the supplement in Elphaba's system, in mg/ml, t minutes after it is administered is given by the formula T(t) = where a and b are constants. Sat³ b(t-6)² + 10 for 0 ≤t≤5 for 5 <t≤7 a. Given that T(t) is DIFFERENTIABLE, find a and b. Give your answers in EXACT FORM, i.e., a FRACTION. You do not need to use the limit definition to compute derivatives in this problem or any problem from now on unless said so explicitly in the instructions. (Hint: Remember that for a function to be differentiable, it needs to also be CONTINUOUS.) b. Using (either of) the values for a and b you found in part a, find the EQUATION FOR THE TANGENT LINE to the graph of y = T(t) at t = 5. Write the terms in the equation in EXACT FORM, i.e., with FRACTIONS. c. Find the INSTANTANEOUS RATE OF CHANGE of the concentration of the supplement in Elphaba's system at t = 2. Include units.
Transcribed Image Text:3. Elphaba the squirrel, the notorious criminal, is planning a prison escape. To aid her in her escape, her friend Walt has concocted a supplement that will make her stronger and more agile. The concentration 7(t) of the supplement in Elphaba's system, in mg/ml, t minutes after it is administered is given by the formula T(t) = where a and b are constants. Sat³ b(t-6)² + 10 for 0 ≤t≤5 for 5 <t≤7 a. Given that T(t) is DIFFERENTIABLE, find a and b. Give your answers in EXACT FORM, i.e., a FRACTION. You do not need to use the limit definition to compute derivatives in this problem or any problem from now on unless said so explicitly in the instructions. (Hint: Remember that for a function to be differentiable, it needs to also be CONTINUOUS.) b. Using (either of) the values for a and b you found in part a, find the EQUATION FOR THE TANGENT LINE to the graph of y = T(t) at t = 5. Write the terms in the equation in EXACT FORM, i.e., with FRACTIONS. c. Find the INSTANTANEOUS RATE OF CHANGE of the concentration of the supplement in Elphaba's system at t = 2. Include units.
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