Which statements are true about the graph of the function f(x) = 6x – 4 + x2? Check all that apply.
2 answers:
You might be interested in
Answer:
a)
b)
Step-by-step explanation:
Assuming the complete question : "A town has a population of 1000 people at time t = 0. In each of the following cases, write a formula for the population, P, of the town as a function of year t. (a) The population increases by 50 people a year. (b) The population increases by 5% a year."
Part a
For this case we can use a linear model in order to estimate the population size since we have a fixed increase each year. So our model would be given by:
Where on this case since represent the increase per year of the slope for the linear model. And the initial amount is
, so then the model is:
Part b
For this case we have a rate of increase and when we have this the lineal model is not the most appropiate. So then we can use an exponential model given by:
Where represent the initial population and for this case b is the rate of increase
since each year we have an increase of 5% and t is the time. So then the model is given by:
Answer:
Option C is correct.
Step-by-step explanation:
An exponential function is of the form: ....[1] where a is the initial value, x is any real number and b is the growth factor
Also, the b value (growth factor) has been replaced either by (1 + r) or by (1 - r).
Then, the growth "rate" (r) is determined as b = 1 + r.
and the decay "rate" (r) is determined as b = 1 - r
- If b> 1, then it is exponential growth function.
- if 0<b< 1. then it is exponential decay function.
Also, b = 1+ 4
Given the equation:
On comparing given equation with [1] we get;
a = 50 and b = 1.15
Since, b = 1.15 > 1
Therefore, the given equation represents the exponential growth.
(A)
Yes, this equation represents the exponential growth.
(B)
Initial value (a) = 50
(C)
Here growth factor, b = 1.15
and
1+ r = 1.15.
⇒