• Initial population is 2600
,• T,he function represents growth.
,• The population size changes each hour by 2%.
STEP - BY - STEP EXPLANATION
What to find?
• The initial population size.
,• To determine whether the function represents growth or decay.
,• Percentage change per hour.
Given:
[tex]p(t)=2600(1.02)^t[/tex]Part A
To determine the initial population size, simply compare the given function with the general formula below:
[tex]P(t)=a(1+r)^t[/tex]Where a is the initial population.
Observe that a = 2600
Therefore, the initial population is 2600
Part B
To know whether the function represents growth or decay, simply observe the value of 1.02.
Clearly 1.02 is greater than 1.
This implies that as t increases, 1.02^t also increases and hence P(t) increases.
Therefore, the function represents growth.
Part C
To find at what percent the population size change each hour;
Since the function represents an exponential growth, compare P(t) =2600(1.02)^t with P(t) = (1+r)^t.
We can see that 1 + r = 1.02
Solve for r.
r = 1.02 - 1
r =0.02
Multiply the value by 100%
r = 0.02 * 100%
r =2 %
Therefore, the population size changes each hour by 2%.
