Real World Exponential Equations

 Halle deposited $4000 into an account that earns 5% interest each year.  The growth of her investment can be expressed by the exponential equation, A = 4000(1 + .05)^t, where A is the amount in the account after t years.  In how many years will her account exceed $10,000?

The equation of an exponential function is given as follows: $$f\left(x\right)=100\left(1.2\right)^x$$  . What is the initial value of the function?

The equation of an exponential function is given as follows: f(x)=100(1.2)^x . Does this equation represent exponential growth or decay and what is the exponential growth or decay rate?

The equation of an exponential function is given as follows: f\left(x\right)=8\left(0.75\right)^x . Does this equation represent exponential growth or decay and what is the exponential growth or decay rate?

The population of Leavetown is 123000 and is decreasing at a rate of 2.3% each year. The exponential equation that represents the population of Leavetown after x years is $$p\left(x\right)=123000\left(0.977\right)^x$$ .

When will the population drop below 80,000 thousand (to the nearest year)? (a)  

What will the population of Leavetown be in 50 years from now (round to the nearest whole number)? ​ ​ (b)  

The function  c(x) = 50 ⋅ (1.08)^x models the cost in dollars, c, of 1 ounce of a certain chemical used in a laboratory.  x represents the number of years since 2005.

How much does an ounce of the chemical cost in 2024?

(round appropriately for the money amount)

A population of bacteria doubles every hour. If the initial population is 500, which function models the population after $$x$$ hours?

The amount of downloads for an album on iTunes, g(d), where d is the number of days since the album was first uploaded can be represented as
g(d) = 5^1.5d
How many downloads will the album have after 3 days?

An experiment begins with 20 grams of a radioactive isotope. This isotope has a half-life. If y is the mass in grams remaining after x half-lives have elapsed, which equation represents the amount of grams the isotope will weigh after 4 half-lives?

The population of wolves in an area is represented by the function $$y=800\left(0.95\right)^x$$  where x is the number of years since the year 2000. 

How many wolves are there in 2011?