Please does anyone know how to solve this in need help asap

We will simplify this (for now) to put only a single variable, x, into the exponent: ex . The function ex is
generally referred to as “the” exponential function, or the natural exponential function.
It is similar to other exponential functions like 2x , 3x , and 7x , only using the number e as the base of the
exponential function (the bases of the functions listed are 2, 3, and 7, respectively).
In class, we used the function A = P 􀀀1 + r
n
nt
to describe the growth of a bacterial colony that had offspring
every hour. This is not a very realistic use of this equation, since bacteria replicate continuously. Thus, the
continuously compunded function, A = Pert , is a more realistic function to use for the growth of a colony of
bacteria.
• 5.) If 100,000 bacteria are in a colony and replicate at a rate of 4% per hour, compute the number of
bacteria in the colony after 2 days (48 hours) if:
– The bacteria replicate every hour
– The bacteria replicate continuously
6 The Natural Logarithm and Computing the Variable r
In math, whenever we create a new function, we must also create its inverse function, the function that will
“undo” that function. We need this to solve for variables that are in our equations.
Just like subtracting 5 is the inverse of adding 5, or dividing by 3 is the inverse of multiplying by 3, we need
something that will “kill off” our new function ex .
We define the natural logarithm to be the inverse function of our new function, ex . We write the natural
logarithm function as ln(x) . The natural logarithm kills off the natural exponential function so that:
eln(x) = x AND ln(ex) = x
Here is an example: Let’s suppose that $2,300 is placed into a continuously compounded account. After 7 years,
there is $2,701.78 in the account. We want to determine the APY, given by the variable, r in the continuously
compounded interest equation: A = Pert .
We plug in the numbers that we know to get:
2, 701.78 = 2, 300er·7
If we want to solve for r, we look at the order of operations that are being applied to r, and their inverse functions:
Multiply by 7 Divide by 7
The exponential function The Natural Logarithm
Multiply by 2,300 Divide by 2,300