PLEASE HELP ME ASAP !!! JUST ANSWER ONE OR BOTH PLEASE HELP!!

1) A population of 370,000 toads is expected to shrink at a rate of 4.3% per year.
Which is the best prediction for the toad population in 11 years?
A) 288,157
B) 159,100
C)35,148
D) 32,190

2) In 2010, a city population was 49,339 and it was declining at a rate of 1.06% each year.
Which is the best prediction for when the city's population will first be below 35,000?
A) 2036
B)2039
C) 2042
D) 2045

Use equation [tex]A=P(1-r)^{t} [/tex]

Question 1: Need to find A:
[tex]A=370,000(1-0.043)^{11} =228157.[/tex]

Question 2: Need to find t, use LOGARITHM:
[tex]1-r=1-0.0106=0.9894 \\ log( \frac{A}{P})=tlog(0.9894) [/tex]
A=35000
P=49339
[tex] \frac{A}{P}=0.7093779769 \\ \frac{log(0.7093...)}{log(0.9894} =t[/tex]
[tex]32.221104307=t=32years.[/tex]
So 2010+32 = 2042.

Answer Link

jainveenamrata jainveenamrata · Answer 2 · 2022-04-27T07:40:55+02:00

The population of the toad is 288,157 then the correct option is A. And in 2042 the population will be 35,000 then the correct option is C.

What is an exponent?

Exponential notation is the form of mathematical shorthand which allows us to write complicated expressions more succinctly. An exponent is a number or letter is called the base. It indicates that the base is to raise to a certain power. X is the base and n is the power.

1) A population of 370,000 toads is expected to shrink at a rate of 4.3% per year. Then the best prediction for the toad population in 11 years will be

[tex]\rm A = 370000(1-0.043)^{11}\\\\A = 288157[/tex]

2) In 2010, the city population was 49,339 and it was declining at a rate of 1.06% each year. Then the best prediction for when the city's population will first be below 35,000 will be

[tex]\begin{aligned} \ln \dfrac{35000}{49339} &= t \ln (1 - 0.0106)\\\\-0.3433&= -0.0106t\\\\t &= 32.386 \approx 32 \ years \end{aligned}[/tex]

Then

→ 2010 + 32 = 2042

More about the exponent link is given below.

https://brainly.com/question/5497425