Question

For the function, supply a valid technology formula.

r(x) = 30 (1 + 1/3.8)^4x

30*(1 + 1/3.8)^(−4*x)

30*(1 + 1/3.8)^(4*x)   

30*(1 + 1/3.8)*(4*x)

30*(1 + 3.8)*(4*x)

30*(1 + 3.8)^(−4*x)

x	−3	−2	−1	0	1	2	3
r(x)

Then use technology to compute the missing values in the table accurate to four decimal places.

Answer 1

solution:-

THE TECHNOLOGY FORMULA IS:-

30*(1+1/3.8)^(4*x)

now we have to find out the values of r(x) for the given values of x using the above technology formula:-

detailed step wise calculation is given below:-

r(-3) = 30*(1+1/3.8)^(4*(-3)) = 30*(1+0.263157)^(-12) = 30*(1.263157)^(-12) = 30*(0.060638) = 1.8181

r(-2) = 30*(1+1/3.8)^(4*(-2)) = 30*(1+0.263157)^(-8) = 30*(1.263157)^(-8) = 30*(0.154291) = 4.6287

r(-1) = 30*(1+1/3.8)^(4*(-1)) = 30*(1+0.263157)^(-4) = 30*(1.263157)^(-4) = 30*(0.392799) = 11.7839

r(-0) = 30*(1+1/3.8)^(4*0) = 30*(1+0.263157)^(0) = 30*(1.263157)^(0) = 30*(1) = 30

r(1) = 30*(1+1/3.8)^(4*1) = 30*(1+0.263157)^(4) = 30*(1.263157)^(4) = 30*(2.545829) = 76.3751

r(2) = 30*(1+1/3.8)^(4*2) = 30*(1+0.263157)^(8) = 30*(1.263157)^(8) = 30*(6.481248) = 194.4385

r(3) = 30*(1+1/3.8)^(4*3) = 30*(1+0.263157)^(12) = 30*(1.263157)^(12) = 30*(16.500154) = 495.0088

x	-3	-2	-1	0	1	2	3
r(x)	1.8181	4.6287	11.7839	30	76.3751	194.4385	495.0088

NOTE:- the final values of value of r(x) are calculated using scientific calculator and are correct upto 4 decimal places.