f(t)=100(1.1)^(3t) Which of the following is an equivalent form of the function f in which the exponent is t ? Choose 1 answer: (A) f(t)=100(1.331)^(t) (B) f(t)=100(3.3)^(t) (c) f(t)=100(4.1)^(t) (D) f(t)=300(1.1)^(t)

Given Function Manipulation: We are given the function f(t) = 100(1.1)^(3t) and we need to find an equivalent form where the exponent is just t. To do this, we need to manipulate the exponent so that it is no longer multiplied by 3.Exponent Property Application: We know that (a^(m))^n = a^(m*n). Using this property, we can rewrite the exponent 3t as t by finding a new base that, when raised to the power of t, is equivalent to (1.1)^(3t).Finding New Base: To find the new base, we calculate (1.1)^3 since this is the value that will be raised to the power of t to give us the equivalent form.Calculate (1.1)^3: Now we calculate (1.1)^3 = 1.1 * 1.1 * 1.1.Multiplication Calculation: Performing the multiplication, we get 1.1 * 1.1 * 1.1 = 1.331.Equivalent Form Calculation: Now we can write the equivalent form of the function as f(t) = 100(1.331)^(t).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

f(t)=100(1.1)^(3t)
Which of the following is an equivalent form of the function
f in which the exponent is
t ?
Choose 1 answer:
(A)
f(t)=100(1.331)^(t)
(B)
f(t)=100(3.3)^(t)
(c)
f(t)=100(4.1)^(t)
(D)
f(t)=300(1.1)^(t)

$f(t)=100(1.1)^{3 t}$ $\newline$ Which of the following is an equivalent form of the function $f$ in which the exponent is $t$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $f(t)=100(1.331)^{t}$ $\newline$ (B) $f(t)=100(3.3)^{t}$ $\newline$ (C) $f(t)=100(4.1)^{t}$ $\newline$ (D) $f(t)=300(1.1)^{t}$

View step-by-step help

Home

Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

f(t)=100(1.1)^{3 t}

\newline

Which of the following is an equivalent form of the function

f

in which the exponent is

t

\newline

Choose

1

answer:

\newline

(A)

f(t)=100(1.331)^{t}

\newline

(B)

f(t)=100(3.3)^{t}

\newline

(C)

f(t)=100(4.1)^{t}

\newline

(D)

f(t)=300(1.1)^{t}

Given Function Manipulation: We are given the function $f(t) = 100(1.1)^{3t}$ and we need to find an equivalent form where the exponent is just $t$ . To do this, we need to manipulate the exponent so that it is no longer multiplied by $3$ .
Exponent Property Application: We know that $(a^{m})^{n} = a^{m*n}$ . Using this property, we can rewrite the exponent $3t$ as $t$ by finding a new base that, when raised to the power of $t$ , is equivalent to $(1.1)^{3t}$ .
Finding New Base: To find the new base, we calculate $(1.1)^3$ since this is the value that will be raised to the power of $t$ to give us the equivalent form.
Calculate $(1.1)^3$ : Now we calculate $(1.1)^3 = 1.1 \times 1.1 \times 1.1$ .
Multiplication Calculation: Performing the multiplication, we get $1.1 \times 1.1 \times 1.1 = 1.331$ .
Equivalent Form Calculation: Now we can write the equivalent form of the function as $f(t) = 100(1.331)^{t}$ .