Suppose j is an exponential function Use the table below to

Suppose j is an exponential function. Use the table below to answer the following questions. Evaluate j(0) Define the function j. What is the 1-unit growth factor? Solve for f when j(f) = 178. f =. Evaluate j^-1 (178)

Solution

writing the exponential equation from the data given

y = ab^x

1.4 = a (b)^.5-------------------- equation 1

.98 = a(b)^1 ------------ equation 2

dividing the two eauations

1.4 = ab^.5 / .98 = ab^1

1.4285 = b^-.5

solving for b

b = .49004

a = 1.9998

therefore, exponential equation becomes

j(f) = 1.9998 (.49004)^f

a) j(0)

plug f = 0

j(0)= 1.998

b) j is an exponetial growth function

c) growth factor is .49004

d) j(f) = 178

1.9998 (.49004)^f = 178

(.49004)^f = 178 / 1.9998

f = ln ( 178 / 1.9998 ) / ln (.49004)

f = - 6.27