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. a. Evaluate j(0) b. Define the function j. c. What is the 1-unit growth factor? d. Solve for f when j(f) = 262. e. Evaluate j^-1 (262)

Solution

f

0.5

1

1.5

2.5

j(f)

1.4

0.98

0.686

0.33614

Let j(f) = A*e^(B*f)

Then   1.4 = A*e^0.5*B = Ae^0.5B

And     0.98 = A*e^(1*B) = Ae^B

Solving both ========> A = 2   ,        B = -0.713

j(f) = A*e^(B*f) = 2*e^(-0.713*f)

a) j(0) = 2

b) j(f) = A*e^(B*f) = 2*e^(-0.713*f)

c) Growth factor = e = 2.71

d) 262 = 2*e^(-0.713*f) ======> f = -6.84

f	0.5	1	1.5	2.5
j(f)	1.4	0.98	0.686	0.33614