9.13 Apps Involving Exponential and Log Function Day 3 HW

Front

What is the exponential function for a savings account that starts with $400 and gains 3% every year?

Back

f(x)=400(1+0.03)^x

Front

How long will it take for half of 130 milligrams of caffeine to be eliminated from the body if it is eliminated at a rate of 11% per hour?

Back

t=5.948 hours

Front

If the population of mosquitoes grows at a rate of 25% a month and reaches 9766 after 4 months, what was the initial population?

Back

4000 mosquitoes

Front

What will be the population of a city in 2015 if it was 120,000 in 1910 and grows at a rate of 1.5% per year?

Back

572949

Front

What is the solution to the equation log_9(x) + log_9(x+2) = log_9(35)?

Back

5

Front

Define exponential growth.

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to growth that accelerates over time.

Front

What is the formula for exponential decay?

Back

f(t) = f_0 * e^(-kt), where f_0 is the initial quantity, k is the decay constant, and t is time.

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power to obtain a given number. For example, in log_b(a), b is the base.

Front

What does it mean for a function to be logarithmic?

Back

A logarithmic function is the inverse of an exponential function, and it describes the time needed to reach a certain level of growth.

Front

How do you convert an exponential equation to logarithmic form?

Back

If a^b = c, then log_a(c) = b.