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The National Ignition Facility at the Lawrence Livermore National Laboratory maintains the world's largest laser facility. The lasers, which are used to start a nuclear fusion reaction, are powered by a capacitor bank that stores a total of about 400 megajoules of energy. When the lasers are fired the capacitors discharge completely and then immediately begin recharging. The charge Q of the capacitors t seconds after the discharge is given by the following formula. Q(t) = Qo(1 - e-t/a) (The maximum charge capacity is Qo, and t is measured in seconds.) (a) Find a formula for the inverse of this function. (Use Q for Q(t).) t = Explain its meaning. This formula gives the charge a achieved at a given time t after a discharge. This formula gives the time t needed after discharge to obtain a given charge a. This formula gives the time t needed after a discharge to obtain a given charge Q. ○ This formula gives the charge Q achieved at a given time t after a discharge. This formula gives the charge Qo achieved at a given time t after a discharge. (b) How long (in s) does it take to recharge the capacitors to 80% of capacity if a = 40? (Round your answer to one decimal place.)

The National Ignition Facility at the Lawrence Livermore National Laboratory maintains the world's largest laser facility. The lasers, which are used to start a nuclear fusion reaction, are powered by a capacitor bank that stores a total of about 400 megajoules of energy. When the lasers are fired the capacitors discharge completely and then immediately begin recharging. The charge Q of the capacitors t seconds after the discharge is given by the following formula. Q(t) = Qo(1 - e-t/a) (The maximum charge capacity is Qo, and t is measured in seconds.) (a) Find a formula for the inverse of this function. (Use Q for Q(t).) t = Explain its meaning. This formula gives the charge a achieved at a given time t after a discharge. This formula gives the time t needed after discharge to obtain a given charge a. This formula gives the time t needed after a discharge to obtain a given charge Q. ○ This formula gives the charge Q achieved at a given time t after a discharge. This formula gives the charge Qo achieved at a given time t after a discharge. (b) How long (in s) does it take to recharge the capacitors to 80% of capacity if a = 40? (Round your answer to one decimal place.)

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter6: Exponential And Logarithmic Functions
Section6.1: Exponential Functions
Problem 60SE: The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is...
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The National Ignition Facility at the Lawrence Livermore National Laboratory maintains the world's largest laser facility. The lasers, which are used to start a nuclear fusion reaction, are powered by a capacitor bank that stores a total of about 400 megajoules of energy. When the lasers are fired the capacitors discharge completely and then immediately begin recharging. The charge Q of the capacitors t seconds after the discharge is given by the following formula. Q(t) = Q(1 - e-t/a) (The maximum charge capacity is Qo, and t is measured in seconds.) (a) Find a formula for the inverse of this function. (Use Q for Q(t).) t = Explain its meaning. This formula gives the charge a achieved at a given time t after a discharge. This formula gives the time t needed after a discharge to obtain a given charge a. This formula gives the time t needed after a discharge to obtain a given charge Q. This formula gives the charge Q achieved at a given time t after a discharge. This formula gives the charge Qo achieved at a given time t after a discharge. оо (b) How long (in s) does it take to recharge the capacitors to 80% of capacity if a = 40? (Round your answer to one decimal place.) S
Transcribed Image Text:The National Ignition Facility at the Lawrence Livermore National Laboratory maintains the world's largest laser facility. The lasers, which are used to start a nuclear fusion reaction, are powered by a capacitor bank that stores a total of about 400 megajoules of energy. When the lasers are fired the capacitors discharge completely and then immediately begin recharging. The charge Q of the capacitors t seconds after the discharge is given by the following formula. Q(t) = Q(1 - e-t/a) (The maximum charge capacity is Qo, and t is measured in seconds.) (a) Find a formula for the inverse of this function. (Use Q for Q(t).) t = Explain its meaning. This formula gives the charge a achieved at a given time t after a discharge. This formula gives the time t needed after a discharge to obtain a given charge a. This formula gives the time t needed after a discharge to obtain a given charge Q. This formula gives the charge Q achieved at a given time t after a discharge. This formula gives the charge Qo achieved at a given time t after a discharge. оо (b) How long (in s) does it take to recharge the capacitors to 80% of capacity if a = 40? (Round your answer to one decimal place.) S
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