exponential functions. need help.?

Question

w.r.t x

a)
y = 16^(x^2 + 2x - 5) = (2x + 2)16^(x^2 + 2x - 5)ln(12)

b)
f(t) = 600,000e^(.4(sqrt(t))

t = time

at what rate is this function growing when t=8?

f(8) = 600,000(-.4)e^(.4sqrt(8))ln(e)
f(8) = 600,000(-.4)e^(1.13)

would this be correct? id appreciate any help/comments on this. thanks.

Answer 1

In (a), don't you want the second part to read:
y' = (2x + 2)*16^(x^2 + 2x - 5)ln(16)
?

In (b) I get
f'(t) = 6.0e5 * exp(.4*sqrt(t)) * (0.4 * 0.5/sqrt(t))

f'(8) ~= 6.0e5 * 0.0707 * exp (1.13)

Note the difference between 0.0707 and (-0.4). You should have noticed that the function would not be decreasing since you have an exponential of an increasing function (.4*sqrt(t)) of t.