Question #f8df9

1 Answer
Gió
May 11, 2016

I found: #color(red)(P(t)=2560e^(0.017185t))# in million of units

Explanation:

If I got the question right (i didn`t get point 2 though!) we can write our equation as:
#P(t)=2560e^(at)# in million of units
So at #t=0#, i.e. 1950, we get:
#P(0)=2560e^(a*0)=2560e^0=2560# million.

To find the constant #a# we use the population in 1960 corresponding to #t=10# getting:

#P(10)=3040=2560e^(10a)#

rearranging and taking the natural log of both sides:

#3040/2560=e^(10a)#
#ln(3040/2560)=ln(e^(10a))#
#ln(3040/2560)=10a#
so that: #a=0.017185#

and your final function will be:

#color(red)(P(t)=2560e^(0.017185t))# in million of units

and

#P(70)=2560e^(0.017185*70)=8524.6# in million of units

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