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course Mth 173
7/11 5:30
Determine the average rate of change of the function y(t) = .1 t 2 + 30 t + -10 between x and x + `dx.What are the growth rate, growth factor and principal function P(t) for an initial investment of $ 870 which is compounded annually at 5% interest?
y(x) = .1 x^2 + 30x + -10
y(x + ‘dx) = .1 (x + ‘dx)^2 + 30(x + ‘dx) + -10
= (x + ‘dx)(x + ’dx) = (x^2 + ‘dxx + ‘dxx + ‘dx^2)
= .1 (x^2 + 2’ddx + ‘dx^2) + 30x + 30’dx + -10
= .1x^2 + .2’ddx + .1’dx^2 + 30’dx + -10
(.1 x^2 + 30x + -10) / (.1x^2 + .2’ddx + .1’dx^2 + 30’dx + -10)
= .1’dx^2 + .2’ddx + 30’dx
The growth rate is .05.
The growth factor is 1.05
The growth function is P(t) = P0 (1.05)^t
&#This looks very good. Let me know if you have any questions. &#