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Fofino [41]
2 years ago
12

Thang decided to borrow ​$ from his local bank to help pay for a car. His loan was for 3 years at a simple interest rate of ​%.

How much interest will Thang​ pay? Thang will pay ​$ nothing interest.
Mathematics
1 answer:
Allisa [31]2 years ago
4 0

Answer: $1080

Step-by-step explanation:

Here is the complete question:

Thang decided to borrow ​$6000 from his local bank to pay for a car. His loan was for 3 years at a simple interest rate of 6​%. How much will he pay.

The formula to calculate simple interest is: (P × R × T)/100

where,

P = Principal = $6000

R = rate = 6%

T = time = 3 years

Simple interest = (P × R × T)/100

= (6000 × 6 × 3)/100

= 108000/100

= $1080

The simple interest is $1080

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2 years ago
A marine biologist monitors the population of sunfish in a small lake. He records 800 sunfish in his first year, 600 sunfish in
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Answer:

Let's use the variable y to represent the number of years passed since the first year.

The population on the first year (y = 0) was 800

The population in the second year (y = 1) was 600.

The ratio in which the population decreased can be calculated as:

R = 600/800 = 0.75

This means that 600 is the 75% of 800, this also means that between the first year and the second year, the population decreased by the 25%

Now let's look at the ratio between the second and third year (y = 2), the population the third year was 450

Now the ratio is:

R = 450/600 = 0.75

Same as before, then we already can see that the population will decrease by 25% each year.

The generic exponential decay equation is:

f(y) = A*(1  - r)^y

where:

A = initial population, in this case, is 800

y = our variable, in this case, represents the number of years

r = the amount that decreases per each unit of our variable, this must be written in decimal form. In this case, we know that the population decreases by 25% each year, and 25% written in decimal form is 0.25

Also, (1 - r) = R, where R is the ratio we found earlier.

To do this, we just divide 25% by 100% to get (25%/100% = 0.25)

Then our equation will be:

f(y) = 800*(1 - 0.25)^y

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1) We want to predict when the population will be 200.

to do this, we set:

f(y) = 200 = 800*( 0.75)^y

and solve it for y.

(200/800) = 0.75^y

(1/4) = 0.75^y

Now we can use the relationship:

Ln(a^x) = x*ln(a)

Then let's apply Ln( ) in both sides to get

ln(1/4) = y*ln(0.75)

ln(1/4)/ln(0.75) = y = 4.8 years.

This means that 4.8 years after the first year, the population will be around 200.

2) The population in the 25 th year (this is 24 years after the first one, so we take y = 24) is:

f(24) = 800*(0.75)^(24) = 0.80

Around this point, we will have no more sunfish in the lake.

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