<img src="https://tex.z-dn.net/?f=p%28t%29%3D5000%283%2Bt%29%5E2%5C%5C%5C%5Cp%27%28t%29%3D%20%5Clim_%7Bh%20%5Cto%200%7D%5C%2C%20%5Cfrac%7Bp%28t%2Bh%29-p%28t%29%7D%7Bh%7D" />
Determine desde los límites la fórmula de la razón de crecimiento de la población en cualquier tiempo t.
<img src="https://tex.z-dn.net/?f=p%27%28t%29%3D%5Clim_%7Bh%20%5Cto%200%7D%5C%2C%20%5Cfrac%7Bp%28t%2Bh%29-p%28t%29%7D%7Bh%7D%5C%5C%5C%5C%3D%5Clim_%7Bh%20%5Cto%200%7D%5C%2C%20%5Cfrac%7B5000%283%2Bt%2Bh%29%5E2-5000%283%2Bt%29%5E2%7D%7Bh%7D%5C%5C%5C%5C%3D%5Clim_%7Bh%20%5Cto%200%7D%5C%2C%20%5Cfrac%7B5000%28t%5E2%2B2ht%2B6t%2Bh%5E2%2B6h%2B9%29-5000%289%2B6t%2Bt%5E2%29%7D%7Bh%7D%5C%5C%5C%5C%3D%5Clim_%7Bh%20%5Cto%200%7D%5C%2C%20%5Cfrac%7B5000%282ht%2Bh%5E2%2B6h%29%2B5000%289%2B6t%2Bt%5E2%29-5000%289%2B6t%2Bt%5E2%29%7D%7Bh%7D%5C%5C%5C%5C%3D%5Clim_%7Bh%20%5Cto%200%7D%5C%2C%20%5Cfrac%7B5000%282ht%2Bh%5E2%2B6h%29%7D%7Bh%7D%5C%5C%5C%5C%3D%5Clim_%7Bh%20%5Cto%200%7D%5C%2C%20%5Cfrac%7B5000h%282t%2Bh%2B6%29%7D%7Bh%7D%5C%5C%5C%5C%3D%5Clim_%7Bh%20%5Cto%200%7D%5C%2C%205000%282t%2Bh%2B6%29%5C%5C%5C%5C%3D5000%282t%2B%280%29%2B6%29%5C%5C%5C%5C%3D5000%286%2B2t%29%3D%5Cboxed%7B10000%283%2Bt%29%7D" />
calcule la razón de crecimiento para t = 30 minutos y para t = 4 horas.
Las unidades de t en la formula son horas : <img src="https://tex.z-dn.net/?f=%5Ctext%7Bt%3D30%20minutos%3D0.5%20h%7D%5C%5C%5C%5Cp%27%28t%29%3D10000%283%2Bt%29%5C%5C%20p%27%280.5%29%3D10000%283%2B0.5%29%3D%5Cboxed%7B35000%7D%5C%5C%5C%5C%5C%5Ct%3D4%5C%2Ch%5C%5C%5C%5Cp%27%28t%29%3D10000%283%2Bt%29%5C%5Cp%27%284%29%3D10000%283%2B4%29%3D%5Cboxed%7B70000%7D" />.