Question

Need some ASAP!!!!!!!!

Answer 1

Exponential function are functions that use exponents or power of an argument

Radioactive substance

The remaining amount after one year

The given parameters are:

Initial, a = 200

Rate, r = 2% loss

The remaining after a year is calculated as:

Remaining = a * (1 - r)

This gives

Remaining = 200 * (1 - 2%)

Evaluate the difference

Remaining = 200 * 0.98

Evaluate the product

Remaining = 196

Hence, the remaining amount after one year is 196 kg

The single number of the product in (a)

In (a), we have:

Remaining = 200 * 0.98

Remove the initial value

Single = 0.98

This represents the multiplying factor.

Hence, the single number of the product in (a) is 0.98

The exponential function

We have:

Initial, a = 200

Multiplying factor, b = 0.98

An exponential function is represented as:

A(t) = ab^t

So, we have:

A(t) = 200 * 0.98^t

Hence, the exponential function is A(t) = 200 * 0.98^t

Time to reach half life

In (c), we have:

A(t) = 200 * 0.98^t

The half life is when

A(t) = 0.5 * A = 0.5 * 200 = 100

So, we have:

100 = 200 * 0.98^t

Divide both sides by 200

0.5 = 0.98^t

Take the logarithm of both sides

log(0.5) = t * log(0.98)

Divide both sides by log(0.98)

t = 34 (approximated)

Hence, the time to reach the half life is 34 years

Population of a town in 10 years

The given parameters are:

• Initial, a = 12500
• Rate, r = 4% decrease

An exponential function is represented as:

A(t) = a(1 - t)^t

So, we have:

A(t) = 12500(1 - 4%)^t

In 10 years, t = 10.

So, we have:

A(10) = 12500(1 - 4%)^10

Evaluate

A(10) = 8310

Hence, the population of the town in 10 years is (d) 8310

Amount of water in a soil

The equation of the amount of water

The given parameters are:

• Initial, a = 4
• Rate, r = 30% decrease

An exponential function is represented as:

A(t) = a(1 - t)^t

So, we have:

A(t) = 4(1 - 30%)^t

Evaluate the difference

A(t) = 4 * 0.7^t

Hence, the equation of the water is A(t) = 4 * 0.7^t

The graph of the function

The domain is given as:

[0,10]

See attachment for the graph of A(t) = 4 * 0.7^t in the domain [0,10]

Read more about exponential functions at:

brainly.com/question/2456547

#SPJ1