Can someone please help me with this question? This is a method of substitution. ASAP?!!!!

The population of a culture of bacteria has a growth rate given by p'(t) = bacteria per hour, forte 0, where r>1 is a real number. The increase in the population over the time interval [0,t] is given by (t + 1)r t Jp'(s)ds. (Note that the growth rate decreases in time, reecting the competition for food and space.) Complete steps (a) through (e) below. 0 3. Using the population model with r= 2, what is the increase in the population over the time interval 0 $154? The increase in the population over the given interval is approximately 168 bacteria. (Round down to the nearest integer as needed.) b. Using the population model with r= 3, what is the increase in the population over the time interval 0 Sta 6'? The increase in the population over the given interval is approximately 102' bacteria. (Round down to the nearest integer as needed.) e. Let AP be the increase in the population over a xed time interval [0,11 For xed T, does AP increase or decrease with the parameter r'? Explain. T * 21 _ ' . A. AP = dt; decreases as r Increases u. .ur d. A lab technician measures an increase in the population of 300 bacteria over the first 15-hr period [0, 15]. Estimate the value of r that best fits this data point. r (Round to the nearest thousandth as needed.)