What is the logarithmic form and the number of days?

Question

After a television advertising campaign ended, sales of Genapet fell rapidly,with daily sales given by S=3200e^-0.08x dollars, where x is the number of days after the campaign ended. 

a) Write the logarithmic form of this function.

b) Use the logarithmic form of this function to find the number of days after the end of the campaign that passed before the sales fell to $2145.

Answer 1

Starting at Michael J.'s b)
ln 2145 = ln 3200e-0.08x
ln 2145 = ln 3200 + ln e-0.08x
ln 2145 = ln 3200 - 0.08x
7.6615 ≈ 8.0709 - 0.08x
-0.4094 ≈ - 0.08x
5.11 ≈ x

Answer 2

Since we have the constant e, will use natural logarithms.

 

a)

 

Natural log both sides of the equation to find S.

 

ln(S) = ln(3200e^-0.08x)

 

 

b)

 

Bring down the exponent as the coefficient of the ln. 

 

ln(2145) = -0.08xln(3200)e

 

 

Divide both sides of equation by -0.08ln(3200)e.

 

x = (ln(2145)) / (-0.08ln(3200)e)

 

x = 4.37