MATH SOLVE

2 months ago

Q:
# Pls help soon:)The graph below shows the total number of known cases of a virus over the weeks since the outbreak began.The curve of best fit to model the data is given below.y= 28, 141 (1.19)^xUse the exponential model to complete the following statements. Round to the nearest whole number, if necessary.There were initially ______ known cases of the virus.There were ______ known cases of the virus after six weeks.There were approximately 135,000 known cases after ______ weeks.

Accepted Solution

A:

Correct answers are:

(1) 28, 141 known cases

(2) 79913.71 known cases after six weeks (round off according to the options given)

(3) After approx. 9 weeks (9.0142 in decimal)

Explanations:

(1) Put x = 0 in given equation

y= 28, 141 (1.19)^x

y= 28, 141 (1.19)^(0)

y= 28, 141

(2) Put x = 6 in the given equation:

y= 28, 141 (1.19)^x

y= 28, 141 (1.19)^(6)

y= 79913.71

(3) Since

y= 28, 141 (1.19)^x

And y = 135,000

135,000 = 28, 141 (1.19)^x

135,000/28, 141 = (1.19)^x

taking "ln" on both sides:

ln(4.797) = ln(1.19)^x

ln(4.797) = xln(1.19)

x = 9.0142 (in weeks)

(1) 28, 141 known cases

(2) 79913.71 known cases after six weeks (round off according to the options given)

(3) After approx. 9 weeks (9.0142 in decimal)

Explanations:

(1) Put x = 0 in given equation

y= 28, 141 (1.19)^x

y= 28, 141 (1.19)^(0)

y= 28, 141

(2) Put x = 6 in the given equation:

y= 28, 141 (1.19)^x

y= 28, 141 (1.19)^(6)

y= 79913.71

(3) Since

y= 28, 141 (1.19)^x

And y = 135,000

135,000 = 28, 141 (1.19)^x

135,000/28, 141 = (1.19)^x

taking "ln" on both sides:

ln(4.797) = ln(1.19)^x

ln(4.797) = xln(1.19)

x = 9.0142 (in weeks)