Question

y=ae^(bx) and passes through two points (-3,80) and 3,0.2) Determine the exact values of the sonstants a and b

Answer 1

80 = ae^(-3b)
0.2 = ae^(0.2b)

divide equation 1 by equation 2:

80/0.2 = ae^(-2b)/ae^(0.2b)

so 400 = e^(-1.8b)

so -1.8b = ln(400)

so b = -ln(400)/1.8

thus a = 80*e^(3b) = 80*e^(-3ln(400)/1.8) = 80*e^(ln(400^(-3/1.8)))

a = 80 * 400^(-3/1.8)

Answer 2

not quite sure your numbers are correct. equation #2 should read 0.2 = ae^(3b)