Answer:
The exponential growth function is ![P=145380e^{0.04103t}](https://tex.z-dn.net/?f=P%3D145380e%5E%7B0.04103t%7D)
Step-by-step explanation:
Given: The population of a certain city was 145,380 in 2000 and 219,135 in 2010.
To find: exponential growth function that models the growth of the city
Solution:
The exponential growth function is given by ![P=P_0 e^{kt}](https://tex.z-dn.net/?f=P%3DP_0%20e%5E%7Bkt%7D)
Here, P denotes total population after time t
denotes initial population
k denotes rate of growth
t denotes time
As
,
![145380=P_0e^{0}\\145380=P_0\\P=145380e^{kt}](https://tex.z-dn.net/?f=145380%3DP_0e%5E%7B0%7D%5C%5C145380%3DP_0%5C%5CP%3D145380e%5E%7Bkt%7D)
As ![P(10)=219135](https://tex.z-dn.net/?f=P%2810%29%3D219135)
![219135=145380e^{10k}\\e^{10k}=\frac{219135}{145380}\\=1.507326\\k=\frac{1}{10}\ln (1.507326)\\=0.04103\\\Rightarrow P=145380e^{0.04103t}](https://tex.z-dn.net/?f=219135%3D145380e%5E%7B10k%7D%5C%5Ce%5E%7B10k%7D%3D%5Cfrac%7B219135%7D%7B145380%7D%5C%5C%3D1.507326%5C%5Ck%3D%5Cfrac%7B1%7D%7B10%7D%5Cln%20%281.507326%29%5C%5C%3D0.04103%5C%5C%5CRightarrow%20P%3D145380e%5E%7B0.04103t%7D)
Substitute the value for y as 450
450=-5x+1
Solve for x
450-1=-5x
449=-5x
89.8=-x
x=-89.8
Answer:
6 quarters
Step-by-step explanation:
6 quarters = 1.50
So that would leave 17 dimes left
And 17 dimes left equal 1.70
1.50 + 1.70 = 3.20
Answer: 6 inches
Step-by-step explanation:
z < 1.25
I used mathaway it's correct