a forestry service developed the following exponential function to determine the steepness factor:
s(x)=Ce^kx
S is the steepness factor
x is the measure of the angle, in degrees, on which fire travels
C and k are constants
their research showed the steepness factor was 1837 when a fire travels on an angle of 10 degrees and 3320 when a fire travels on an angle of 20 degree. what was their equation for S(x)? show the work that leads to your answer. the work must include the use of logarithms, and the calculations not use rounded or trncated values.

Question

a forestry service developed the following exponential function to determine the steepness factor:
s(x)=Ce^kx
S is the steepness factor 
x is the measure of the angle, in degrees, on which fire travels
C and k are constants
their research showed the steepness factor was 1837 when a fire travels on an angle of 10 degrees and 3320 when a fire travels on an angle of 20 degree. what was their equation for S(x)? show the work that leads to your answer. the work must include the use of logarithms, and the calculations not use rounded or trncated values.

campbell_st · Answer

well the 2 equations are 

$$1837 = Ce^{10k}$$

and 

$$3320 = C e^{20k}$$

you will need to solve these simultaneously 

make C the subject in the 1st equation 

$$C = \frac{1837}{e^{10k}}$$

and substitute it into the 2nd equation. This will allow you to solve for k

$$3320 = \frac{1837}{e^{10k}} \times e^{20k} $$

which simplifies to 

$$3320 = 1837 \times e^{10k}$$

so 

$$\frac{3320}{1837} = e^{10k}$$

take the ln of both sides

$$\ln(\frac{3320}{1837}) = 10k$$

which means 

$$k = \frac{1}{10} \times \ln(\frac{3320}{1837})$$

when you have evaluated k

substitute it into either of the initial equations to find  C

hope this helps

anonymous · Answer

Thanks!:)