f(x)=ab^x
In this equation, a is the initial value and b is the multiplier. From the exercise, we know that the current cost is $2.75. Also, since the cost is increasing by 5 % per year, we can write this as a multiplier by adding the decimal form of 5 % to 1.
1+5/100=1+0.05=1.05
By substituting a= 2.75 and b= 1.05 into the exponential function, we can write our equation.
f(x)= 2.75( 1.05)^x
To calculate the cost of the loaf of bread 10 years from now, we have to substitute x=10 in the equation and simplify.
b The current population is 42 000, and the population is expected to decrease by 25 % each year over the next five years. Since the population is decreasing, we can write this as a multiplier by subtracting the decimal form of 25 % from 1.
1-25/100=1-0.25=0.75By substituting a= 42 000 and b= 0.75 into the general form of an exponential function, we can write our equation.
f(x)= 42 000( 0.75)^x
To calculate the population in 5 years, we have to substitute x=5 in the equation and simplify.
c The annual multiplier b is the factor we have to multiply the original value by ten times (once per year) to obtain the final value. With this information, we can write the following equation.
