# Math and Science Solutions for Businesses/Exponentiell equation

Question
An elephant weighs 120 kg after 7 days , after 30 days it weights 150kg, how much does the elephant weights after 150 days after it's born? When it's always exponential

Looks like we want to use an exponential to model the elephant's weight gain. This can be written as

W(t) = B･exp(at)

where t is time (in days), A = growth constant and B = initial weight of elephant (when it was born; i.e., weight W(0) = B when t = 0).

We have 2 'data points' to use to determine the 2 parameters A and B. These are

W(7) = 120 = B･exp(7A)

W(30) = 150 = B･exp(30A).

Now its just a matter of a little algebra to find A and B. It looks like we can make some progress by taking the (natural) log of the 2 equations to get (after dividing by B)

ln(120/B) = 7A  --> ln(120) - ln(B) = 7A  (using the property of logs that ln(x/y) = ln(x) - ln(y) ) --> ln(B) = ln(120) - 7A

ln(150/B) = 30a  --> ln(150) - ln(B) = 30A or ln(B) = ln(150) - 30A

Setting the 2 expressions for ln(B) equal to each other gives

ln(120) - 7A = ln(150) - 30A  --> a few algebra steps -->  ln(150/120)/23 = A  --> a ≈ 0.01.

So now we know the parameter A. To get B, plug this value into one of the previous expressions for ln(B) and exponentiate to get

B = exp{ln(120) - 7A) = 120･exp(-0.07) ≈ 112.

With the 2 parameters determined, we can evaluate

W(150) = 112･exp{(0.01)･150) = 502 kg.

Math and Science Solutions for Businesses

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#### Randy Patton

##### Expertise

Questions regarding application of mathematical techniques and knowledge of physics and engineering principles to product and services design, optimization, prediction, feasibility and implementation. Examples include sales and product performance projections based on math/physics models in addition to standard regression; practical and cost effective sensor design and component configuration; optimal resource allocation using common tools (eg., MS Office); advanced data analysis techniques and implementation; simulation and "what if" analysis; and innovative applications of remote sensing.

##### Experience

26 years as professional physical scientist and project manager for elite research company providing academic quality basic and applied research for government and defense industry clients (currently retired). Projects I have been involved in include: - Notional sensor performance predictions for detecting underwater phenomena - Designing and testing guidance algorithms for multi-component system - Statistical analysis of ship tracking data and development of anomaly detector - Deployed vibration sensors in Arctic ice floes; analysis of data - Developed and tested ocean optical instrument to measure particles - Field testing of protoype sonar system - Analysis of synthetic aperture radar system data for ocean surface measurements - Redesigned dust shelters for greeters at Burning Man Festival Project management with responsibility for allocation and monitoriing of staff and equipment resources.

Publications
“A Numerical Model for Low-Frequency Equatorial Dynamics” (with Mark A. Cane), J. of Phys. Oceanogr., 14, No. 12, pp. 18531863, December 1984.

Education/Credentials
MIT, MS Physical Oceanography, 1981 UC Berkeley, BS Applied Math, 1976

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Am also an Expert in Advanced Math and Oceanography