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Math · Advanced Math
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Action potential in neurons Dendrites Neurons (nerve cells) are the core components of the nervous system. They provide critical functions such as controlling muscle activity, sensing, thinking, remembering, and regulating glandular secretions. Electrical signals and chemical messengers are used to transmit and receive information between them. The neurons consist of: Soma Nucleus Axon .The cell body (soma) and its processes. Dendrites: the branched projections of a neuron that act to propagate the electrochemical stimulation received from other neural cells to the cell body. The axon: a nerve fibre that conducts electrical impulses away from the cell body to signal other neurons. As a nerve impulse travels down the axon, the change in voltage v of a neuron with respect to time follows the differential equation du 0.01t -1.0+1+0.02t over the course of 100 ms, where t is measured in milliseconds and v in millivolts. We start at v(0)-70 mV
v(0)-70 mV (a) Integrate the previous differential equation to express voltage as a function of time, v(t), and sketch its graph for t e [0,100] (b) What is the voltage after 100 ms? A neuron in your brain sends a charge down an 80 cm long axon toward your hand at a speed of 10 m per second. At the time when the charge reaches your elbow, the voltage in the axon is -70 mV except on the 6 cm long piece between 47 and 53 cm from your brain. On this piece, the voltage is v(x)-70.0+10.019.0 - (x - 50.0)21 where v(x) is the voltage (in mV) at a distance of x centimeters from the brain. (c) How long will it take the information to get to your hand? How long did it take to reach your elbow?» (d) Sketch a graph of the voltage along the whole axon.
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