Question

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)^x


Use 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.

Answer 1

Im so confused about the guys answer above can someone explain it or just tell me the answer to the question pls

Explanation:

Answer 2

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)