A function g(x) increases by a factor of 1.15 over every unit interval in x and g(0)=1.Which could be a function rule for g(x)?
Question
A function g(x) increases by a factor of 1.15 over every unit interval in x and g(0)=1.
Which could be a function rule for g(x)?
Solution
The function g(x) is increasing by a factor of 1.15 over every unit interval in x. This suggests that the function is exponential, because exponential functions increase by a constant factor over equal intervals.
The general form of an exponential function is g(x) = ab^x, where a is the initial value and b is the growth factor.
Given that g(0) = 1, we can substitute these values into the equation to find a.
1 = a*b^0 Since any number to the power of 0 is 1, a = 1.
The growth factor b is given as 1.15.
So, the function rule for g(x) could be g(x) = 1*1.15^x, or simplified to g(x) = 1.15^x.
Similar Questions
A function g(x) increases by 0.4 over every unit interval in x and g(0)=1.Which could be a function rule for g(x)?
A function f(x) increases by a factor of 1.9 over every unit interval in x and f(0)=2.Which could be a function rule for f(x)?
Let g(x) be the indicated transformation(s) of f (x) = x. Write the rule for g(x) .15. vertical stretch by a factor of 4
A function h(t) increases by 0.15 over every unit interval in t and h(0)=0.Which could be a function rule for h(t)?
A function h(t) increases by a factor of 10 over every unit interval in t and h(0)=1.Which could be a function rule for h(t)?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.