Question

Question #f8df9

Answer 1

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