Rewrite each fuinctgion in the form y A0eatfor appropriate

Rewrite each fuinctgion in the form y = A_0e^at,for appropriate constants A_0 and a. (Round A_0 and a to four decimal places as necessary.) y = 19(4^t) y = 2 (1/8)^t y = -5(1.578) ^t -1 y = -14(2.003)^-t y = 4(12.28)^3t

Solution

1)y=19(4^t)

y=19(e^(ln4)t)

y=19(e^1.3863t)

2)y=2(1/8)^t

y=2e^(ln(1/8))t

y=2e^-2.0794t

3)y =-5(1.578)^t-1

y =-(5/1.578)(1.578)^t

y =-(5/1.578)(e^ln1.578)^t

y =-3.1686e^0.4562t

d)y=-14(2.003)^-t

y=-14(1/2.003)^t

y=-14e^{ln(1/2.003) t}

y=-14e^-0.6946t

e)y=4(12.28)^3t

y=4(1851.8)^t

y=4e^(ln1851.8)t

y=4e^{7.5239 t}