Answer: See Below
<u>Step-by-step explanation:</u>
y = a(b)ˣ where
- a: initial population (starting point)
- b: growth rate
- x: number of hours
- y: final population
<u>Part 1 </u>
Given: a = 1, b = 1.5 → y = 1(1.5)ˣ
![\begin{array}{c|c|c||c|l}\underline{\quad a\quad}&\underline{\quad b\quad}&\underline{\quad x\quad}&\underline{\ \ a(b)^x=}&\underline{y\quad\quad}\\\1&1.5&5&1(1.5)^5=&7.6\quad\rightarrow \bold{7}\\1&1.5&10&1(1.5)^{10}=&57.7\quad\rightarrow \bold{57}\\1&1.5&15&1(1.5)^{15}=&437.9\quad\rightarrow \bold{437}\\1&1.5&20&1(1.5)^{20}=&3,325.2\quad\rightarrow \bold{3,325}\\\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bc%7Cc%7Cc%7C%7Cc%7Cl%7D%5Cunderline%7B%5Cquad%20a%5Cquad%7D%26%5Cunderline%7B%5Cquad%20b%5Cquad%7D%26%5Cunderline%7B%5Cquad%20x%5Cquad%7D%26%5Cunderline%7B%5C%20%5C%20a%28b%29%5Ex%3D%7D%26%5Cunderline%7By%5Cquad%5Cquad%7D%5C%5C%5C1%261.5%265%261%281.5%29%5E5%3D%267.6%5Cquad%5Crightarrow%20%5Cbold%7B7%7D%5C%5C1%261.5%2610%261%281.5%29%5E%7B10%7D%3D%2657.7%5Cquad%5Crightarrow%20%5Cbold%7B57%7D%5C%5C1%261.5%2615%261%281.5%29%5E%7B15%7D%3D%26437.9%5Cquad%5Crightarrow%20%5Cbold%7B437%7D%5C%5C1%261.5%2620%261%281.5%29%5E%7B20%7D%3D%263%2C325.2%5Cquad%5Crightarrow%20%5Cbold%7B3%2C325%7D%5C%5C%5Cend%7Barray%7D)
Given: a = 1, b = 1.5, y = 500,000
to take over Antelope Valley
<u>Part 2</u>
Given a = 1, b = 2 → y = 1(2)ˣ
![\begin{array}{c|c|c||c|l}\underline{\quad a\quad}&\underline{\quad b\quad}&\underline{\quad x\quad}&\underline{\ \ a(b)^x=}&\underline{y\quad\quad}\\\1&2&5&1(2)^5=&\bold{32}\\1&2&10&1(2)^{10}=&\bold{1024}\\1&2&15&1(2)^{15}=&\bold{32,768}\\1&2&20&1(2)^{20}=&\bold{1,048,576}\ \rightarrow \text{exceeds population}\\\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bc%7Cc%7Cc%7C%7Cc%7Cl%7D%5Cunderline%7B%5Cquad%20a%5Cquad%7D%26%5Cunderline%7B%5Cquad%20b%5Cquad%7D%26%5Cunderline%7B%5Cquad%20x%5Cquad%7D%26%5Cunderline%7B%5C%20%5C%20a%28b%29%5Ex%3D%7D%26%5Cunderline%7By%5Cquad%5Cquad%7D%5C%5C%5C1%262%265%261%282%29%5E5%3D%26%5Cbold%7B32%7D%5C%5C1%262%2610%261%282%29%5E%7B10%7D%3D%26%5Cbold%7B1024%7D%5C%5C1%262%2615%261%282%29%5E%7B15%7D%3D%26%5Cbold%7B32%2C768%7D%5C%5C1%262%2620%261%282%29%5E%7B20%7D%3D%26%5Cbold%7B1%2C048%2C576%7D%5C%20%5Crightarrow%20%5Ctext%7Bexceeds%20population%7D%5C%5C%5Cend%7Barray%7D)
Given: a = 1, b = 2, y = 500,000
to take over Antelope Valley
Answer: 30 miles
Step-by-step explanation:A typical car can travel 30 miles on just one gallon of gasoline
8x+4=9x-5
when you solve that out you get x =9
then you plug in x everywhere in the chart
3(9)=27
9(9)-5=76
180-76-27= 77°
angle E =77°
please mark brainiest if you can
Given:
Base of a right triangle = 7 in
Height of a right triangle = a
Hypotenuse = 16 in
To find:
The length of side a.
Solution:
Using Pythagoras theorem:
In right triangle, square of the hypotenuse is equal to the sum of the squares of the other two sides.
![7^2+a^2=16^2](https://tex.z-dn.net/?f=7%5E2%2Ba%5E2%3D16%5E2)
![49+a^2=256](https://tex.z-dn.net/?f=49%2Ba%5E2%3D256)
Subtract 49 from both sides.
![49+a^2-49=256-49](https://tex.z-dn.net/?f=49%2Ba%5E2-49%3D256-49)
![a^2=207](https://tex.z-dn.net/?f=a%5E2%3D207)
Taking square root on both sides, we get
a = 14.4
The length of side a is 14.4 in.