Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
For species A,
![P =2000e^{0.05t}](https://tex.z-dn.net/?f=P%20%3D2000e%5E%7B0.05t%7D)
For species B,
![P =5000e^{0.02t}](https://tex.z-dn.net/?f=P%20%3D5000e%5E%7B0.02t%7D)
When their populations are equal,
![\begin{array}{rcl}2000e^{0.05t} & = & 5000e^{0.02t}\\e^{0.05t} & = & 2.5e^{0.02t}\\0.05t & = & \ln2.5 + 0.02t\\0.05t & = & 0.9163 + 0.02t\\0.03t & = & 0.9163\\t& = & \dfrac{0.9163}{0.03}\\\\& = & \mathbf{30.54}\\\end{array}\\\text{The populations of species A and B will be the same in $\large \boxed{\textbf{30.54 yr}}$}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcl%7D2000e%5E%7B0.05t%7D%20%26%20%3D%20%26%205000e%5E%7B0.02t%7D%5C%5Ce%5E%7B0.05t%7D%20%26%20%3D%20%26%202.5e%5E%7B0.02t%7D%5C%5C0.05t%20%26%20%3D%20%26%20%5Cln2.5%20%2B%200.02t%5C%5C0.05t%20%26%20%3D%20%26%200.9163%20%2B%200.02t%5C%5C0.03t%20%26%20%3D%20%26%200.9163%5C%5Ct%26%20%3D%20%26%20%5Cdfrac%7B0.9163%7D%7B0.03%7D%5C%5C%5C%5C%26%20%3D%20%26%20%5Cmathbf%7B30.54%7D%5C%5C%5Cend%7Barray%7D%5C%5C%5Ctext%7BThe%20populations%20of%20species%20A%20and%20B%20will%20be%20the%20same%20in%20%24%5Clarge%20%5Cboxed%7B%5Ctextbf%7B30.54%20yr%7D%7D%24%7D)
The diagram below shows the population of Species A overtaking that of Species B in about 30.5 yr.
We will guess and check to solve this problem
504/9= 56
504/8= 63
504/7= 72
504/6= 84
.....
we can continue the pattern. However, we know that 50 is the product of 8 and 7, so we can use that number
9*8*7=504
Answer:
yes
Step-by-step explanation:
We can estimate* that the total price including tax of the game will be less than ...
$43.31 +10% of 43.31 = $43.31 +4.33 = $47.61
Todd easily has enough to pay for the game, including tax.
_____
You can work this more exactly a couple of ways.
1. Price + tax = 1.085×$43.31 = $46.99 . . . less than Todd's budget
2. Most Todd can afford: $55.50/1.085 = $51.15 . . . more than the game price
_____
* For estimating purposes, we like to use numbers that are easy to compute with. 10% is one such number, as it only requires moving the decimal point.
Step-by-step explanation:
7.50= (1 + x/100 ) × 5.50
7.50/ 5.50 = 1+x/100
x/100 = 0.36
x= 36.36%