a function grows exponentially at a rate of 10%. If the value at t=2 is 908.56 what is the value of (a) in the formula: f(x)=a.b(x)
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To find the value of "a" in the formula f(x)=a.b(x), we need to use the given information: the function grows exponentially at a rate of 10% and the value at t=2 is 908.56.
In an exponential growth formula, the general form is given by f(x) = a*(1 + r)^x, where "a" is the initial value, "r" is the growth rate as a decimal, and "x" is the time or period.
Since we know that the function grows at a rate of 10% or 0.10, we can rewrite the formula as follows:
f(x) = a*(1 + 0.10)^x
Now we can substitute the values given in the problem. We are told the value at t=2 is 908.56, so we can write:
908.56 = a*(1 + 0.10)^2
Simplifying further:
908.56 = a*(1.10)^2
We can calculate (1.10)^2 to find its value:
(1.10)^2 = 1.21
Substituting this back into the equation:
908.56 = a*1.21
Now we solve for "a" by dividing both sides of the equation by 1.21:
a = 908.56 / 1.21 = 750.5
Therefore, the value of "a" in the formula f(x) = a*b(x) would be 750.5.